ML Aggarwal Class 10 Maths Solutions Chapter 03 Shares and Dividends

Question 1. Find the dividend received on 60 shares of Rs.20 each if 9% dividend is declared.
Answer: To find the dividend on one share, multiply the face value by the dividend rate: \( 9\% \text{ of } Rs.20 = \frac{9}{100} \times 20 = Rs.1.8 \). Since there are 60 shares, the total dividend is \( Rs.1.8 \times 60 = Rs.108 \).
In simple words: For each share worth Rs.20, you get Rs.1.8 as dividend. So 60 shares give you Rs.1.8 × 60 = Rs.108.

Exam Tip: Always identify the face value, dividend rate, and number of shares separately before multiplying them together.

Question 2. A company declares 8 percent dividend to the share holders. If a man receives Rs.2840 as his dividend, find the nominal value of his shares.
Answer: Let the nominal value of shares be Rs.x. According to the problem, 8% of x equals Rs.2840. Set up the equation: \( \frac{8}{100} \times x = 2840 \). Solving for x: \( x = \frac{2840 \times 100}{8} = \frac{284000}{8} = Rs.35500 \). Therefore, the nominal value of the man's shares is Rs.35500.
In simple words: If 8% of something gives Rs.2840, then the full amount is 2840 divided by 8 and multiplied by 100, which is Rs.35500.

Exam Tip: When dividend received is given, use the formula: Nominal Value = (Dividend × 100) ÷ Rate to find the face value.

Question 3. A man buys 250, ten-rupee shares each at Rs.12.50. If the rate of dividend is 7%, find the: (a) dividend he receives annually. (b) percentage return on his investment.
Answer:
(a) The nominal (face) value per share is Rs.10. The market value per share is Rs.12.50. With 250 shares purchased, the total nominal value is \( 250 \times 10 = Rs.2500 \). At a 7% dividend rate, the annual dividend works out to: \( \frac{7}{100} \times 2500 = Rs.175 \).
(b) The amount spent on buying shares is \( 250 \times 12.50 = Rs.3125 \). The return percentage is calculated by: \( \frac{175}{3125} \times 100 = \frac{17500}{3125} = 5.6\% \). So the percentage return on his investment is 5.6%.
In simple words: The dividend depends on the face value (Rs.10), not the price paid (Rs.12.50). The return percentage shows how much money you earn compared to what you spent.

Exam Tip: Remember that dividend is always calculated on nominal value, while return percentage is based on the market value (amount actually invested).

Question 4. Find the market price of 5% Rs.100 share when a person gets a dividend of Rs.65 by investing Rs.1430.
Answer: Let the number of shares purchased be x. The nominal value per share is Rs.100, and the dividend rate is 5%. Using the dividend formula: \( 65 = x \times \frac{5}{100} \times 100 \). Simplifying: \( 65 = 5x \), so \( x = 13 \). Since the total investment is Rs.1430 for 13 shares, the market price per share is: \( \frac{1430}{13} = Rs.110 \).
In simple words: If 5% of Rs.100 gives Rs.5 per share, and the total dividend is Rs.65, then there are 13 shares. The market price is the total money spent divided by the number of shares.

Exam Tip: When dividend amount and investment amount are both given, find the number of shares first, then divide investment by number of shares to get market price.

Question 5. Govind buys 50 shares of face value Rs.100 available at Rs.132. (i) What is his investment? (ii) If the dividend is 7.5% p.a., what will be his annual income? (iii) If he wants to increase his annual income by Rs.150, how many extra shares should he buy?
Answer:
(i) The total investment is the number of shares multiplied by the market value per share: \( 50 \times 132 = Rs.6600 \). Therefore, Govind's investment is Rs.6600.
(ii) Annual income is calculated using the face value and dividend rate: \( 50 \times \frac{7.5}{100} \times 100 = Rs.375 \). So Govind's annual income is Rs.375.
(iii) If he wants to increase his income by Rs.150, his new annual income will be \( Rs.375 + Rs.150 = Rs.525 \). Let the new number of shares be x. Then: \( 525 = x \times \frac{7.5}{100} \times 100 \), which gives \( 525 = 7.5x \), so \( x = 70 \). The extra shares he needs to buy are \( 70 - 50 = 20 \) shares.
In simple words: Investment uses the market price. Annual income uses the face value. To buy extra shares for more income, find the new total number needed, then subtract the shares already owned.

Exam Tip: Keep track of the difference between market value (buying price) and nominal value (for dividend calculation). The same dividend rate applies to any number of shares.

Question 6. A lady holds 1800, Rs.100 shares of a company that pays 15% dividend annually. Calculate her annual dividend. If she had bought these shares at 40% premium, what percentage return does she get on her investment?
Answer: The annual dividend is found using: \( 1800 \times \frac{15}{100} \times 100 = Rs.27000 \). Since shares are bought at 40% premium, the market value per share is: \( 100 + \left(\frac{40}{100} \times 100\right) = 100 + 40 = Rs.140 \). The total investment becomes: \( 1800 \times 140 = Rs.252000 \). The percentage return is: \( \frac{27000}{252000} \times 100 = \frac{2700}{252} = \frac{75}{7} = 10\frac{5}{7}\% \).
In simple words: When you buy shares at a premium (higher than face value), you spend more money but get the same dividend, so your return percentage drops.

Exam Tip: For premium and discount problems, always recalculate the investment amount first, then use the return formula: (Annual Income ÷ Investment) × 100.

Question 7. What sum should a person invest in Rs.25 shares, selling at Rs.36, obtain an income of Rs.720, if the dividend declared is 12%? Also find the percentage return on his income.
Answer: Let the number of shares purchased be x. The nominal value per share is Rs.25, and the dividend rate is 12%. Using the annual dividend formula: \( 720 = x \times \frac{12}{100} \times 25 \). Simplifying: \( 720 = 3x \), so \( x = 240 \). The total investment required is: \( 240 \times 36 = Rs.8640 \). The percentage return on investment is: \( \frac{720}{8640} \times 100 = \frac{72000}{8640} = \frac{25}{3} = 8\frac{1}{3}\% \).
In simple words: First find how many shares give the desired income. Then multiply by the selling price to get the total amount to invest. Return percentage shows earnings compared to money spent.

Exam Tip: Always find the number of shares first using the dividend and nominal value, then calculate investment using market price.

Question 8. Ashok invests Rs.26400 on 12% Rs.25 shares of a company. If he receives a dividend of Rs.2475, find: (i) the number of shares he bought. (ii) the market value of each share.
Answer:
(i) Let the number of shares purchased be x. Using the dividend formula: \( 2475 = x \times \frac{12}{100} \times 25 \). Simplifying: \( 2475 = 3x \), so \( x = 825 \). Therefore, the number of shares bought is 825.
(ii) The market value per share is calculated by dividing total investment by the number of shares: \( \frac{26400}{825} = Rs.32 \).
In simple words: When you know the total dividend and dividend rate, you can find the number of shares. Then divide the total amount spent by the number of shares to find the price per share.

Exam Tip: In this type of problem, always solve for the number of shares first, then use it to find the market value per share.

Question 9. A man invests Rs.4500 in shares of a company which is paying 7.5% dividend. If Rs.100 shares are available at a discount of 10%, find (i) the number of shares he purchases. (ii) his annual income.
Answer:
(i) The nominal value per share is Rs.100. At a 10% discount, the market value is: \( Rs.100 - \left(\frac{10}{100} \times 100\right) = Rs.100 - Rs.10 = Rs.90 \). The number of shares he can purchase is: \( \frac{4500}{90} = 50 \) shares.
(ii) His annual income using the 7.5% dividend rate on the nominal value is: \( 50 \times \frac{7.5}{100} \times 100 = Rs.375 \).
In simple words: When shares are at a discount, the buying price is lower, so you can buy more shares with the same money. Dividend is still calculated on the face value, not the discounted price.

Exam Tip: With discounts, the money goes further. Calculate the reduced market value first, then find how many shares the investment covers.

Question 10. Amit invests Rs.36000 in buying Rs.100 shares at Rs.20 premium. The dividend is 15% per annum. Find: (i) the number of shares he buys (ii) his yearly dividend (iii) the percentage return on his investment.
Answer:
(i) At Rs.20 premium, the market value per share is: \( Rs.100 + Rs.20 = Rs.120 \). The number of shares he buys is: \( \frac{36000}{120} = 300 \) shares.
(ii) His yearly dividend is: \( 300 \times \frac{15}{100} \times 100 = Rs.4500 \).
(iii) The percentage return is: \( \frac{4500}{36000} \times 100 = \frac{450000}{36000} = \frac{25}{2} = 12.5\% \).
In simple words: A premium means you pay more per share. While the total dividend stays good, your return percentage on the actual money spent is lower than the dividend rate.

Exam Tip: Premium reduces how many shares you can buy with a fixed amount, which affects both dividend income and return percentage calculations.

Question 11. Mr. Gupta invested Rs.33000 in buying Rs.100 shares of a company at 10% premium. The dividend declared by the company is 12%. Find: (a) the number of shares purchased by him. (b) his annual dividend.
Answer:
(a) At 10% premium, the market value per share is: \( Rs.100 + \left(\frac{10}{100} \times 100\right) = Rs.100 + Rs.10 = Rs.110 \). The number of shares purchased is: \( \frac{33000}{110} = 300 \) shares.
(b) The annual dividend is: \( 300 \times \frac{12}{100} \times 100 = Rs.3600 \).
In simple words: Calculate the actual buying price (including premium) first. Then divide the investment by this price to get the number of shares. Finally, use the number of shares and face value to find dividend.

Exam Tip: Always identify whether you are dealing with nominal value (for dividend) or market value (for investment calculations).

Question 12. A man buys shares at the par value of Rs.10 yielding 8% dividend at the end of a year. Find the number of shares bought if he receives a dividend of Rs.300.
Answer: Since shares are bought at par value, the market value per share equals the nominal value per share, which is Rs.10. Let the number of shares purchased be x. Using the dividend formula: \( 300 = x \times \frac{8}{100} \times 10 \). Simplifying: \( 300 = 0.8x \), so \( x = \frac{300 \times 10}{8} = \frac{3000}{8} = 375 \) shares.
In simple words: At par value, you pay exactly the face value with no premium or discount. The dividend works the same way as always.

Exam Tip: "At par" means no premium or discount - the buying price equals the face value.

Question 13. A man invests Rs.8800 on buying shares of face value of rupees hundred each at a premium of 10%. If he earns Rs.1200 at the end of year as dividend, find: (i) the number of shares he has in this company (ii) the dividend percentage per share.
Answer:
(i) The nominal value per share is Rs.100. At 10% premium, the market value is: \( 100 + \left(\frac{10}{100} \times 100\right) = 100 + 10 = Rs.110 \). The number of shares bought is: \( \frac{8800}{110} = 80 \) shares.
(ii) To find the dividend percentage, use the formula: Dividend % = (Annual Dividend ÷ Number of Shares ÷ Nominal Value) × 100. Substituting: \( \frac{1200}{80 \times 100} \times 100 = \frac{1200}{8000} \times 100 = 15\% \). Therefore, the dividend percentage per share is 15%.
In simple words: First find how many shares were purchased using the market price. Then work backwards: divide total dividend by the number of shares and by face value to find the rate.

Exam Tip: When finding dividend percentage, make sure you divide by (Number of Shares × Nominal Value), not by the market value or investment amount.

Question 14. A man invested Rs 45000 in 15% Rs 100 shares quoted at Rs 125. When the market value of these shares rose to Rs 140, he sold some shares, just enough to raise Rs 8400.
(i) The number of shares he still holds.
(ii) The dividend due to him on these shares.
Answer:
(i) The face value per share is Rs 100. At a market price of Rs 125, the total number of shares bought was 45000 ÷ 125 = 360 shares. When shares were sold at the new market price of Rs 140, selling them to get Rs 8400 means 8400 ÷ 140 = 60 shares were sold. The remaining shares he holds = 360 - 60 = 300 shares.

(ii) The annual dividend earned on the remaining 300 shares at the 15% rate on nominal value is: 300 × (15/100) × 100 = Rs 4500.
In simple words: He bought 360 shares at Rs 125 each. He sold 60 shares at Rs 140 each when prices rose. He keeps 300 shares and gets Rs 4500 as yearly profit from them.

Exam Tip: Always separate the number of shares bought (using market value) from the number sold. The dividend is always calculated on the nominal value, not the price paid.

Question 15. Ajay owns 560 shares of a company. The face value of each share is Rs 25. The company declares a dividend of 9%.
(i) The dividend that Ajay will get
(ii) The rate of interest on his investment if Ajay has paid Rs 30 for each share.
Answer:
(i) The yearly dividend Ajay receives is calculated by multiplying the number of shares, the dividend rate, and the face value together: 560 × (9/100) × 25 = Rs 1260.

(ii) Ajay's total investment = 560 × 30 = Rs 16800. His yearly income from dividends = Rs 1260. The rate of return on this investment = (1260/16800) × 100 = 7.5%.
In simple words: Ajay gets Rs 1260 every year as profit from his Rs 16800 investment. This works out to 7.5% return each year.

Exam Tip: Return percentage is always (Annual Income / Amount Invested) × 100. Remember that face value determines the dividend, while market/actual price paid determines the investment amount.

Question 16. A company with 10000 shares of nominal value of Rs 100 declares an annual dividend of 8% to the share holders.
(i) Calculate the total amount of dividend paid by the company
(ii) Ramesh bought 90 shares of the company at Rs 150 per share. Calculate the dividend he received and the percentage return on his investment.
Answer:
(i) The total dividend paid to all shareholders = 10000 × (8/100) × 100 = Rs 80000.

(ii) Ramesh's dividend on 90 shares = 90 × (8/100) × 100 = Rs 720. His total outlay = 90 × 150 = Rs 13500. His return percentage = (720/13500) × 100 = 5⅓%.
In simple words: The company paid Rs 80000 total as profit to all owners. Ramesh spent Rs 13500 and earned Rs 720, which is about 5.33% return on what he paid.

Exam Tip: Distinguish between (a) total company dividend - uses all shares and nominal value, and (b) individual dividend - uses only that person's shares. Return % shows how well the investment performed.

Question 17. A company with 500 shares of nominal value Rs 120 declares an annual dividend of 15%.
(i) The total amount of dividend paid by the company
(ii) The annual income of Mr Sharma who hold 80 shares of the company. If the return percent of Mr. Sharma from his shares is 10%, find the market value of each shares.
Answer:
(i) Total company dividend = 500 × (15/100) × 120 = Rs 9000.

(ii) Mr. Sharma's yearly income = 80 × (15/100) × 120 = Rs 1440. Using the relationship between dividend rate, nominal value, return %, and market value - (15/100) × 120 = (10/100) × M.V. - we get M.V. = (15 × 120)/10 = Rs 180.
In simple words: The company pays Rs 9000 total each year. Mr. Sharma gets Rs 1440 yearly. Each share he bought costs Rs 180 in the market.

Exam Tip: The formula Dividend% × N.V. = Return% × M.V. connects all four variables. If three are known, always find the fourth using this relationship.

Question 18. By investing Rs 7500 in a company paying 10 percent dividend, an income of Rs 500 is received. What price is paid for each Rs 100 share.
Answer: Let x be the number of shares purchased. Since each share has face value Rs 100 and gives 10% dividend, the annual income per share = (10/100) × 100 = Rs 10. With total income of Rs 500, the number of shares = 500 ÷ 10 = 50 shares. The market price paid per share = 7500 ÷ 50 = Rs 150.
In simple words: The investor bought 50 shares and paid a total of Rs 7500, so each share cost Rs 150.

Exam Tip: First find the number of shares using dividend information, then compute market value by dividing total investment by number of shares.

Question 19. A man buys 400 ten-rupee shares at a premium of Rs 2.50 on each share. If the rate of dividend is 8%, find
(i) his investment
(ii) dividend received
(iii) yield.
Answer:
(i) With a nominal value of Rs 10 and a premium of Rs 2.50, the market value = Rs 10 + Rs 2.50 = Rs 12.50 per share. Total investment = 400 × 12.50 = Rs 5000.

(ii) The annual dividend received = 400 × (8/100) × 10 = Rs 320.

(iii) Yield (rate of return) = (320/5000) × 100 = 6.4%.
In simple words: He paid Rs 5000 for 400 shares. Each year he gets Rs 320 back, which equals 6.4% of what he paid.

Exam Tip: Premium is added to face value to get market value. Yield always divides annual income by the amount actually invested (at market price), not by face value.

Question 20. A man invests Rs 10400 in 6% shares at Rs 104 and Rs 11440 in 10.4% shares at Rs 143. How much income would he get in all? (Assume face value of Rs 100)
Answer: In the first investment, he buys 10400 ÷ 104 = 100 shares. With face value Rs 100 and 6% dividend rate, his yearly income = 100 × (6/100) × 100 = Rs 600. In the second investment, he buys 11440 ÷ 143 = 80 shares. With face value Rs 100 and 10.4% dividend rate, his yearly income = 80 × (10.4/100) × 100 = Rs 832. His total yearly income = 600 + 832 = Rs 1432.
In simple words: The first purchase gives him Rs 600 yearly. The second purchase gives him Rs 832 yearly. Combined, he earns Rs 1432 every year.

Exam Tip: When face value is not stated, assume Rs 100 per share. Always calculate shares bought using market value, then calculate dividend using face value and stated rate.

Question 21. Two companies have shares of 7% at Rs 116 and 9% at Rs 145 respectively. In which of the shares would the investment be more profitable? (Assume face value of Rs 100)
Answer: For the first company, each Rs 116 invested brings in 7% of Rs 100 = Rs 7 income yearly. So income per rupee = 7/116. For the second company, each Rs 145 invested brings in 9% of Rs 100 = Rs 9 income yearly. So income per rupee = 9/145. Comparing these ratios by finding a common denominator: 7/116 = 35/580 and 9/145 = 36/580. Since 36/580 is larger, the second company's shares (9% at Rs 145) offer better returns.
In simple words: The second option gives more money back for each rupee you spend. It is the better choice.

Exam Tip: To compare two investments, always calculate income per rupee invested. The higher ratio means better profitability.

Question 22. Which is better investment - 6% Rs 100 shares at Rs 120 or 8% Rs 10 shares at Rs 15
Answer: For the first option, investing Rs 120 produces yearly income of 6% of Rs 100 = Rs 6. Income per rupee = 6/120 = 1/20. For the second option, investing Rs 15 produces yearly income of 8% of Rs 10 = Rs 0.8. Income per rupee = 0.8/15 = 4/75. To compare, use a common denominator: 1/20 = 15/300 and 4/75 = 16/300. Since 16/300 exceeds 15/300, the second option (8% Rs 10 shares at Rs 15) is the better investment.
In simple words: The second option returns more income for each rupee invested, making it the wiser choice.

Exam Tip: Always simplify income per rupee to a common denominator when comparing different share investments. This method works regardless of share face values or prices.

Question 23. A man invests Rs 10080 in 6% hundred-rupee shares at Rs 112. Find his annual income. When the shares fall to Rs 96 he sells out the shares and invests the proceeds in 10% ten-rupee shares at Rs 8. Find the change in his annual income.
Answer: Initially, he buys 10080 ÷ 112 = 90 shares. His yearly income = 90 × (6/100) × 100 = Rs 540. When shares drop to Rs 96, he sells all 90 shares for 90 × 96 = Rs 8640. With this money, he buys shares at Rs 8 each, getting 8640 ÷ 8 = 1080 shares with face value Rs 10 each. His new yearly income = 1080 × (10/100) × 10 = Rs 1080. The change in annual income = 1080 - 540 = Rs 540 (an increase).
In simple words: He earned Rs 540 yearly at first. After switching investments, he earns Rs 1080 yearly. His income doubled, a gain of Rs 540 per year.

Exam Tip: When selling shares and reinvesting, use the proceeds (sale amount) as the new investment capital. Always track nominal value and dividend rate separately from market value to avoid errors.

Question 24. Sachin invests Rs.8500 in 10% Rs.100 shares at Rs.170. He sells the shares when the price of each share rises by Rs.30. He invests the proceeds in 12% Rs.100 shares at Rs.125. Find (i) the sale proceeds. (ii) the number of Rs.125 shares he buys. (iii) the change in his annual income.
Answer: (i) Total investment equals Rs.8500. Since the market value per share is Rs.170, the number of shares purchased equals Rs.8500 divided by Rs.170, which equals 50.

When the price rises by Rs.30, the selling price per share becomes Rs.170 plus Rs.30, which is Rs.200. Therefore, the sale proceeds from 50 shares at Rs.200 each equals Rs.(50 × 200) = Rs.10000.

(ii) The market value of the new shares is Rs.125. So the number of new shares bought equals Rs.10000 divided by Rs.125, which equals 80. Hence, he buys 80 Rs.125 shares.

(iii) For the change in his annual income:

Annual dividend from the first investment (10% Rs.100 shares at Rs.170):
= 50 × (10/100) × 100 = Rs.500

Annual dividend from the new investment (12% Rs.100 shares at Rs.125):
= 80 × (12/100) × 100 = Rs.960

Change in annual income = Rs.960 - Rs.500 = Rs.460. His annual income increased by Rs.460.
In simple words: He sold shares worth Rs.10000. He then bought 80 new shares. His yearly income went up by Rs.460.

Exam Tip: When share prices change, always calculate the new number of shares carefully - mistake here cascades through all income calculations. Verify that both income calculations use the correct nominal value (Rs.100 here, not the market value).

Question 25. A person invests Rs.4368 and buys certain hundred-rupee shares at Rs.91. He sells shares worth Rs.2400 when they have risen to Rs.95 and the remainder when they have fallen to Rs.85. Find the gain or loss on the total transaction.
Answer: Total investment equals Rs.4368. The nominal value per share is Rs.100, and the market value per share is Rs.91. Therefore, the number of shares purchased equals Rs.4368 divided by Rs.91, which is 48 shares.

Since shares worth Rs.2400 (face value) were sold first, the number of such shares equals Rs.2400 divided by Rs.100, which is 24 shares. These 24 shares were sold at Rs.95 each, giving sale value = Rs.(24 × 95) = Rs.2280.

The remaining shares = 48 - 24 = 24 shares. These remaining 24 shares were sold at Rs.85 each, giving sale value = Rs.(24 × 85) = Rs.2040.

Total sale value = Rs.2280 + Rs.2040 = Rs.4320

Gain or Loss = Total sale value - Initial investment = Rs.4320 - Rs.4368 = -Rs.48

Since the total sale value is less than the initial investment, a loss of Rs.48 occurred on the complete transaction.
In simple words: He bought 48 shares for Rs.4368. He sold some at a higher price and some at a lower price. Overall, he lost Rs.48.

Exam Tip: Keep face value and market value distinct - here face value (Rs.100) identifies which shares to count, while market value determines selling proceeds. A common error is confusing these, leading to wrong share counts.

Question 26. By purchasing Rs.50 gas shares for Rs.80 each, a man gets 4% profit on his investment. What rate percent is company paying? What is his dividend if he buys 200 shares?
Answer: Let the rate percent the company pays be x%. The dividend on one share of Rs.50 equals (x/100) × Rs.50 = Rs.(x/2). His profit on one share (which costs Rs.80) equals 4% of Rs.80 = (4/100) × Rs.80 = Rs.3.2 = Rs.(16/5).

Since the dividend on a share must equal the profit earned:
x/2 = 16/5
x = (16/5) × 2 = 32/5 = 6.4

Therefore, the rate percent the company is paying equals 6.4%.

For 200 shares, the annual dividend equals:
200 × (6.4/100) × 50 = 200 × (64/1000) × 50 = 2 × 64 × 5 = Rs.640
In simple words: When you buy shares at Rs.80 and get 4% profit, the company must be paying 6.4% dividend. If you buy 200 shares, your yearly dividend is Rs.640.

Exam Tip: The key insight is that profit percentage on investment equals dividend percentage on face value - this equality lets you solve for the unknown rate. Always work with face value for dividend calculations, never with market value.

Question 27. Rs.100 shares of a company are sold at a discount of Rs.20. If the return on the investment is 15%. Find the rate of dividend declared.
Answer: Let the rate of dividend be x%. The dividend on one share of Rs.100 equals (x/100) × Rs.100 = Rs.x.

Since shares are sold at a discount of Rs.20, the market value of one share = Rs.100 - Rs.20 = Rs.80.

The return on investment is given as 15%, which means:
15 = (x/80) × 100
x = (15 × 80) / 100 = 1200 / 100 = 12

Therefore, the rate of dividend declared equals 12%.
In simple words: When you buy shares at Rs.80 (discount of Rs.20), you need a 15% return. This means the company must pay 12% dividend on the face value.

Exam Tip: The return formula is (Dividend / Market Value) × 100 - never use face value in the denominator for return calculations. This is where most students stumble.

Question 28. A company declared a dividend of 14%. Find the market value of Rs.50 shares if the return on the investment was 10%.
Answer: Let the market value of one share be Rs.x. The dividend on one share of Rs.50 equals 14% of Rs.50 = (14/100) × Rs.50 = Rs.7.

Given that the return on investment is 10%, we have:
10 = (7 / x) × 100
x = (7 × 100) / 10 = 700 / 10 = 70

Therefore, the market value of each Rs.50 share equals Rs.70.
In simple words: The company pays Rs.7 dividend per share. If you want a 10% return, you should pay Rs.70 per share.

Exam Tip: Remember: return percentage = (Annual dividend / Market value) × 100. A premium share (market value higher than face value) gives lower return even at the same dividend rate - this is a key exam concept.

Question 29. A company with 10000 shares of Rs.100 each, declares an annual dividend of 5%. (i) What is the total amount of dividend paid by the company? (ii) What would be the annual income of a man, who has 72 shares, in the company? (iii) If he received only 4% on his investment, find the price he paid for each share.
Answer: (i) Total dividend = Number of shares × Dividend rate × Face value per share
= 10000 × (5/100) × 100 = Rs.50000
The total dividend paid by the company equals Rs.50000.

(ii) Annual income of the man with 72 shares:
= 72 × (5/100) × 100 = Rs.360
His annual income from the company equals Rs.360.

(iii) Let the price he paid for each share be Rs.x. His total investment = Rs.72x.
Given that he received 4% on his investment:
4 = (360 / 72x) × 100
x = (360 × 100) / (4 × 72) = 36000 / 288 = 125
The price he paid for each share equals Rs.125.
In simple words: The company paid out Rs.50000 total. The man made Rs.360 per year. To get 4% return on that Rs.360, he must have paid Rs.125 per share.

Exam Tip: Part (iii) tests whether you understand that return on investment relates actual income to actual amount paid - this is different from dividend rate on face value. Calculate investment from the return formula, not from nominal values.

Question 30. A man sold some Rs.100 shares paying 10% dividend at a discount of 25% and invested the proceeds in Rs.100 shares paying 16% dividend quoted at Rs.80 and thus increased his income by Rs.2000. Find the number of shares sold by him.
Answer: Let the number of shares sold be x. Since shares are sold at a discount of 25%, the selling price per share = Rs.100 - 25% of Rs.100 = Rs.100 - Rs.25 = Rs.75. Total sale proceeds = Rs.75x.

Number of new Rs.100 shares at Rs.80 bought = Rs.75x / Rs.80 = 15x / 16.

Annual dividend from old shares (10% on Rs.100):= x × (10/100) × 100 = Rs.10x

Annual dividend from new shares (16% on Rs.100):= (15x/16) × (16/100) × 100 = Rs.15x

Change in annual income = Rs.15x - Rs.10x = Rs.5x.
Given that income increased by Rs.2000:
5x = 2000
x = 400
The number of shares sold by the man equals 400.
In simple words: He sold old shares at Rs.75 each. He bought new shares at Rs.80 each with the proceeds. His income rose because new shares paid higher dividend. He must have sold 400 shares to get the Rs.2000 increase.

Exam Tip: Set up the equation by expressing the number of new shares in terms of x (the unknown old shares). The discount and premium affect how many new shares you get for your sale proceeds - get this ratio right, or your final answer fails.

Question 31. A man invests Rs.6750, partly in shares of 6% at Rs.140 and partly in shares of 5% at Rs.125. If his total income is Rs.280, how much has he invested in each?
Answer: Let the investment in 6% shares at Rs.140 be Rs.x. Then investment in 5% shares at Rs.125 = Rs.(6750 - x).

Income on one share of Rs.140 = 6% of Rs.100 = Rs.6. Income on Rs.x = Rs.(6x/140) = Rs.(3x/70).

Income on one share of Rs.125 = 5% of Rs.100 = Rs.5. Income on Rs.(6750 - x) = Rs.[(5(6750 - x))/125] = Rs.[(6750 - x)/25].

Total income = Rs.280:
(3x/70) + (6750 - x)/25 = 280

Multiplying through by 350 (LCM of 70 and 25):
15x + 14(6750 - x) = 280 × 350
15x + 94500 - 14x = 98000
x = 3500

Investment in 6% shares at Rs.140 = Rs.3500
Investment in 5% shares at Rs.125 = Rs.6750 - Rs.3500 = Rs.3250
In simple words: He put Rs.3500 into the first type and Rs.3250 into the second type. Together they gave him Rs.280 per year.

Exam Tip: Income per rupee invested varies by share type - do not assume equal incomes. Set up the income equation carefully, using income per rupee = (dividend % on face value) / (market value). Clear fractions early by multiplying by the LCM.

Question 32. Divide Rs.20304 into two parts such that if one part is invested in 9% Rs.50 shares at 8% premium and the other part is invested in 8% Rs.25 shares at 8% discount, then the annual incomes from both the investment are equal.
Answer: Let the investment in 9% Rs.50 shares be Rs.x. Then investment in 8% Rs.25 shares = Rs.(20304 - x).

For 9% Rs.50 shares at 8% premium:
Market value = Rs.50 + 8% of Rs.50 = Rs.50 + Rs.4 = Rs.54
Income on one share = 9% of Rs.50 = Rs.4.5
Income on Rs.x = Rs.(4.5x / 54) = Rs.(x/12)

For 8% Rs.25 shares at 8% discount:
Market value = Rs.25 - 8% of Rs.25 = Rs.25 - Rs.2 = Rs.23
Income on one share = 8% of Rs.25 = Rs.2
Income on Rs.(20304 - x) = Rs.[(2(20304 - x)) / 23] = Rs.[(2(20304 - x)) / 23]

Since incomes are equal:
(x/12) = [2(20304 - x)] / 23
23x = 24(20304 - x)
23x = 487296 - 24x
47x = 487296
x = 10368

Investment in 9% Rs.50 shares at Rs.54 = Rs.10368
Investment in 8% Rs.25 shares at Rs.23 = Rs.20304 - Rs.10368 = Rs.9936
In simple words: He invested Rs.10368 in one type and Rs.9936 in the other type, so both gave him the same yearly income.

Exam Tip: Premium and discount change market value but NOT the face value used for dividend. Set up the income equation using (dividend % on face value) / (market value). Cross-multiply carefully to avoid arithmetic errors with larger numbers.

Question 1. The sum of money required to buy 50, Rs.40 shares at Rs.38.50 is:
(a) Rs.1920
(b) Rs.1924
(c) Rs.1925
(d) Rs.1952
Answer: (c) Rs.1925
In simple words: You buy 50 shares at Rs.38.50 each. Multiply 50 by Rs.38.50 to get the total cost: Rs.1925.

Exam Tip: This is straightforward multiplication - market value times number of shares. Do not confuse market value with face value; the question gives market value directly.

Question 2. If Jagbeer invest Rs.10320 on Rs.100 shares at a discount of Rs.14, then the number of shares he buys is
(a) 110
(b) 120
(c) 130
(d) 150
Answer: (b) 120
In simple words: Nominal value is Rs.100. He buys at a discount of Rs.14, so market value = Rs.100 - Rs.14 = Rs.86 per share. Divide his investment by market value: Rs.10320 / Rs.86 = 120 shares.

Exam Tip: Always subtract discount from face value (or add premium) to find market value. Divide total investment by market value per share, not by face value.

Question 3. If Nisha invests Rs.19200 on Rs.50 shares at a premium of 20%, then the number of shares she buys is
(a) 640
(b) 320
(c) 160
(d) 80
Answer: (c) 160
In simple words: Face value is Rs.50. A 20% premium means she pays 20% more: Rs.50 + (20% of Rs.50) = Rs.50 + Rs.10 = Rs.60 per share. Divide investment by market value: Rs.19200 / Rs.60 = 320 shares.

Exam Tip: Premium adds to face value - do not subtract it. Calculate 20% of face value correctly before adding. Then divide investment (not face value times investment) by the resulting market value.

Question 3. (i) 15 shares of a company of nominal value Rs 75 available at a discount of 20%
Answer: The total amount needed to buy 15 shares is Rs 900. Since each share has a face value of Rs 75 and is being sold at a 20% discount, the market value per share becomes Rs 60. Therefore, the cost of 15 shares is 15 × Rs 60 = Rs 900.
In simple words: When a share at face value Rs 75 is sold at a 20% discount, it costs Rs 60 per share. So 15 shares cost Rs 900 altogether.

Exam Tip: Always calculate the market value first by subtracting the discount from the nominal value, then multiply by the number of shares to find total investment.

Question 4. Rs 40 shares of a company are selling at 25% premium. If Mr. Jacob wants to buy 280 shares of the company, then the investment required by him is
(1) Rs 11,200
(2) Rs 14,000
(3) Rs 16,800
(4) Rs 8,400
Answer: (2) Rs 14,000
In simple words: When shares with a face value of Rs 40 are sold at a 25% premium, each share costs Rs 50. If you buy 280 shares, the total cost is 280 × Rs 50 = Rs 14,000.

Exam Tip: Premium means the market value is higher than the face value. Add the premium to the nominal value to get the actual cost per share.

Question 5. Arun possesses 600 shares of Rs 25 of a company. If the company announces a dividend of 8%, then Arun's annual income is
(1) Rs 48
(2) Rs 480
(3) Rs 600
(4) Rs 1,200
Answer: (4) Rs 1,200
In simple words: Arun gets paid a dividend based on how many shares he owns and what their face value is. With 600 shares worth Rs 25 each and an 8% dividend, he earns Rs 1,200 per year.

Exam Tip: Dividend is always calculated on the nominal value of shares, not the market value. Use the formula: Number of shares × Dividend rate ÷ 100 × Nominal value per share.

Question 6. A man invests Rs 24,000 on Rs 60 shares at a discount of 20%. If the dividend declared by the company is 10%, then his annual income is
(1) Rs 3,000
(2) Rs 2,880
(3) Rs 1,500
(4) Rs 1,440
Answer: (1) Rs 3,000
In simple words: The man buys shares at a reduced price (20% discount from Rs 60 = Rs 48 per share). He can buy 500 shares with his Rs 24,000. At 10% dividend on the face value, he earns Rs 3,000 each year.

Exam Tip: When shares are at a discount, the market value is less than nominal value. Calculate the number of shares he can afford, then compute dividend on the nominal value, not the purchase price.

Question 7. Salman has some shares of Rs 50 of a company paying 15% dividend. If his annual income is Rs 3,000, then the number of shares he possesses is
(1) 80
(2) 400
(3) 600
(4) 800
Answer: (2) 400
In simple words: Work backwards from his yearly income. If he gets Rs 3,000 per year from 15% dividend on Rs 50 shares, he must own 400 shares.

Exam Tip: Use the dividend formula rearranged to find the number of shares: Annual Dividend ÷ (Dividend Rate ÷ 100) ÷ Nominal Value = Number of shares.

Question 8. (i) Shares of company A, paying 12%, Rs 100 shares are at Rs 80.
(ii) Shares of company B, paying 12%, Rs 100 shares are at Rs 100.
(iii) Shares of company C, paying 12%, Rs 100 shares are at Rs 120.
Shares of which company are at premium?
(1) Company A
(2) Company B
(3) Company C
(4) Company A and C
Answer: (3) Company C
In simple words: A share is at premium when its market value is higher than its face value. Only Company C has shares selling at Rs 120, which is more than the Rs 100 face value.

Exam Tip: Premium occurs when market value > nominal value; discount occurs when market value < nominal value; par value means market value = nominal value. Compare the two values directly.

Question 9. The sum invested to purchase 15 shares of a company of nominal value Rs 75 available at a discount of 20% is:
(1) Rs 60
(2) Rs 90
(3) Rs 1,350
(4) Rs 900
Answer: (4) Rs 900
In simple words: Each share has a face value of Rs 75. At a 20% discount, the cost drops to Rs 60 per share. For 15 shares, the total investment is 15 × Rs 60 = Rs 900.

Exam Tip: Always compute the market value first by applying the discount to the nominal value, then multiply by the quantity of shares to get total investment needed.

Assertion-Reason Type Questions

Question. Assertion (A): Dividend, the profit a shareholder receive from the company, depends on the market value.
Reason (R): Dividend is always calculated as the percentage of face value of the share.
(1) Assertion (A) is true, but Reason (R) is false.
(2) Assertion (A) is false, but Reason (R) is true.
(3) Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
(4) Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).
Answer: (2) Assertion (A) is false, but Reason (R) is true
In simple words: Dividends depend on the face value of shares, not their current market price. A 10% dividend means you get 10% of the face value no matter how much you paid to buy the share.

Exam Tip: Remember that dividend percentage applies to nominal value only. Market value affects how much you pay to buy the shares but does not change the dividend amount received.

Question. Assertion (A): The company is in profit.
Reason (R): The above share is at premium.
Quotation: "10% Rs 120 shares at Rs 1,200"
(1) Assertion (A) is true, but Reason (R) is false.
(2) Assertion (A) is false, but Reason (R) is true.
(3) Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
(4) Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).
Answer: (4) Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A)
In simple words: The 10% dividend in the quotation shows the company is earning money. The share is at premium because Rs 1,200 is far higher than its face value of Rs 120. Both facts are true, but the reason doesn't directly cause the assertion.

Exam Tip: The presence of a dividend shows the company has profits, but a premium share price is a separate market phenomenon. They can both be true without one causing the other.

Question. Assertion (A): His total investment is Rs 60,000.
Reason (R): The market value of each share is Rs 40.
A man purchases 1,200 shares of a company of face value Rs 50 at a discount of Rs 10.
(1) Assertion (A) is true, but Reason (R) is false.
(2) Assertion (A) is false, but Reason (R) is true.
(3) Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
(4) Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).
Answer: (2) Assertion (A) is false, but Reason (R) is true
In simple words: When a Rs 50 share is bought at a Rs 10 discount, each share costs Rs 40. With 1,200 shares, the total is 1,200 × Rs 40 = Rs 48,000, not Rs 60,000.

Exam Tip: Subtract the discount amount from the nominal value to get the market value, then multiply by the number of shares. Watch for calculation errors when both quantities are large.

Chapter Test

Question 1. If a man received Rs 1,080 as dividend from 9% Rs 20 shares, find the number of shares purchased by him.
Answer: Suppose the man bought x shares. The annual dividend is calculated as: Number of shares × Dividend rate ÷ 100 × Nominal value per share. So 1,080 = x × 9 ÷ 100 × 20. Solving this, 1,080 = 9x ÷ 5, which gives x = 600. The man bought 600 shares.
In simple words: Use the dividend formula backwards to find how many shares give Rs 1,080 income at 9% on Rs 20 shares. The answer is 600 shares.

Exam Tip: Set up the dividend equation carefully and isolate the variable representing the number of shares, then solve step by step.

Question 2. Find the percentage interest on capital invested in 18% shares when a Rs 10 share costs Rs 12.
Answer: Each share with a face value of Rs 10 gives a dividend of 18% of Rs 10 = Rs 1.80. The investor pays Rs 12 to buy one share. The return percentage is: (Dividend per share ÷ Market value per share) × 100 = (1.80 ÷ 12) × 100 = 15%. So the investor earns 15% return on his investment.
In simple words: The investor gets Rs 1.80 dividend but pays Rs 12 for each share. That works out to 15% of his money coming back as profit every year.

Exam Tip: Return on investment compares the yearly income received to the actual amount of money spent, not the face value of the shares.

Question 3. Mahesh Kulkarni invests Rs 10,000 in 10% Rs 100 shares of a company. If his annual dividend is Rs 800, find:
(i) the market value of each share.
(ii) the rate percent which he earns on his investment.
Answer:
(i) Let the market value per share be x. The number of shares bought is 10,000 ÷ x. Using the dividend formula: 800 = (10,000 ÷ x) × 10 ÷ 100 × 100. Simplifying: 800 = 100,000 ÷ x, so x = 125. The market value of each share is Rs 125.
(ii) The return on investment is: (Annual dividend ÷ Total investment) × 100 = (800 ÷ 10,000) × 100 = 8%. Mahesh earns 8% return on his investment.
In simple words: First, find how many shares he bought by working backward from the dividend. Then find what he paid per share. Finally, divide his yearly income by his total spending to get his return percentage.

Exam Tip: In two-part questions, use the answer to part (i) as a check for part (ii). The numbers should be consistent throughout.

Question 4. At what price should a 9% Rs 100 share be quoted when the money is worth 6%?
Answer: Let the market value be x per share. A 9% Rs 100 share pays a dividend of Rs 9 per share. When money is worth 6%, the investor expects 6% return on his investment. Setting up the equation: (9 ÷ x) × 100 = 6. Solving, 900 = 6x, so x = 150. The share should be quoted at Rs 150.
In simple words: Find the market price at which the dividend you get equals the return rate that investors want. If they want 6% and the dividend is Rs 9, the price must be Rs 150.

Exam Tip: This type of question matches dividend yield to market interest rates. The higher the desired return, the lower the share price, and vice versa.

Question 5. By selling at Rs 92, some 2.5% Rs 100 shares and investing the proceeds in 5% Rs 100 shares at Rs 115, a person increased his annual income by Rs 90. Find:
(i) the number of shares sold.
(ii) the number of shares purchased.
(iii) the new income.
(iv) the rate percent which he earns on his investment.
Answer:
(i) Let x be the number of shares sold. He receives Rs 92x from the sale. The number of new shares bought is 92x ÷ 115. His old income was 2.5% of 100x = 2.5x. His new income is 5% of (92x ÷ 115) × 100 = (460x ÷ 115). The increase is (460x ÷ 115) - 2.5x = 90. Solving: (460x - 287.5x) ÷ 115 = 90, so 172.5x = 10,350, giving x = 60. He sold 60 shares.
(ii) The number of shares purchased is 92 × 60 ÷ 115 = 48 shares.
(iii) The new income is 5% of 48 × 100 = Rs 240.
(iv) His new return is (240 ÷ (92 × 60)) × 100 = (240 ÷ 5,520) × 100 = 4.35% (approximately).
In simple words: The person sold lower-paying shares and bought higher-paying ones. His income rose because even though he bought fewer shares, each paid more dividend. Track the number of shares and income at each step.

Exam Tip: In complex multi-part share problems, organize the given and find information step by step. Track three things: the number of shares, their denomination, and the dividend rate at each stage.

Question 6. A man has some shares of Rs.100 par value paying 6% dividend. He sells half of these at a discount of 10% and invests the proceeds in 7% Rs.50 shares at a premium of Rs.10. This transaction decreases his income from dividends by Rs.120. Calculate: (i) the number of shares before the transaction. (ii) the number of shares he sold. (iii) his initial annual income from shares.
Answer: Let the number of 6% Rs.100 shares held by the man be x. The man sells x/2 shares. Since the 6% Rs.100 shares were at par, the nominal value equals the market value at Rs.100. With a 10% discount on the selling price, each share sells for Rs.100 - Rs.10 = Rs.90. This gives total sales proceeds of 90 × (x/2) = Rs.45x. The 7% Rs.50 shares are bought at a premium of Rs.10, so their market value becomes Rs.50 + Rs.10 = Rs.60. Using the proceeds, the man buys 45x/60 = 3x/4 new shares. Before the transaction, his annual income from x shares was x × (6/100) × 100 = Rs.6x. After the transaction, his income is (x/2) × (6/100) × 100 + (3x/4) × (7/100) × 50 = Rs.3x + Rs.(21x/8) = Rs.(45x/8). The difference in income is 6x - 45x/8 = 120, which gives (48x - 45x)/8 = 120, so 3x/8 = 120, thus x = 320. Therefore, the number of shares before the transaction is 320, the number sold is 160, and the initial annual income is Rs.1920.
In simple words: The man starts with 320 shares. He sells half of them (160 shares) for Rs.90 each. He uses that money to buy 240 new shares at Rs.60 each. This change reduces his yearly dividend income by Rs.120.

Exam Tip: Always set up the income equation carefully by calculating annual dividend before and after the transaction; remember to use the formula (number of shares) × (dividend rate/100) × (nominal value).

Question 7. Divide Rs.101520 into two parts such that if one part is invested in 8% Rs.100 shares at 8% discount and the other in 9% Rs.50 shares at 8% premium, the annual incomes are equal.
Answer: Let the investment in 8% Rs.100 shares be Rs.x, making the investment in 9% Rs.50 shares Rs.(101520 - x). The 8% Rs.100 shares trade at 8% discount, so the market value is Rs.100 - Rs.8 = Rs.92 per share. The 9% Rs.50 shares trade at 8% premium, so their market value is Rs.50 + Rs.4 = Rs.54 per share. The annual income from Rs.x invested at Rs.92 per share is (x/92) × (8/100) × 100 = Rs.2x/23. The annual income from Rs.(101520 - x) invested at Rs.54 per share is [(101520 - x)/54] × (9/100) × 50 = Rs.(101520 - x)/12. Setting these equal: 2x/23 = (101520 - x)/12. Cross-multiplying gives 24x = 2334960 - 23x, so 47x = 2334960, and x = 49680. Therefore, the investment in 8% Rs.100 shares is Rs.49680, and the investment in 9% Rs.50 shares is Rs.51840.
In simple words: You split Rs.101520 two ways. One part buys shares that pay 8% dividend; the other buys shares that pay 9% dividend. Both investments must give you the same yearly income. The split is Rs.49680 and Rs.51840.

Exam Tip: When equating annual incomes, ensure you correctly apply the dividend rate and nominal value separately; a common error is forgetting to divide the investment by the market value first to find the number of shares.

Question 8. A man buys Rs.40 shares of a company which pays 10% dividend. He buys the shares at such a price that his profit is 16% on his investment. At what price did he buy each share?
Answer: Let the market value (purchase price) of 1 share be Rs.x. The dividend on 1 share of nominal value Rs.40 is 10% of Rs.40 = Rs.4. The profit on the investment is defined as the ratio of annual dividend to purchase price, expressed as a percentage. Setting this up: (4/x) × 100 = 16. Solving for x: 4 × 100 = 16x, so 400 = 16x, thus x = 25. Therefore, the man bought each share at Rs.25.
In simple words: Each share has a face value of Rs.40 and pays Rs.4 in yearly dividend. The man wants a 16% return on his money, which means Rs.4 should be 16% of what he pays. Solving this: he must pay Rs.25 per share.

Exam Tip: Remember that profit/return percentage is calculated as (annual dividend / purchase price) × 100; this is not the same as the stated dividend percentage on the nominal value.

Question 9. A person invested 20%, 30% and 25% of his savings in buying shares at par values of three different companies A, B and C which declare dividends of 10%, 12% and 15% respectively. If his total income on account of dividends be Rs.4675, find his savings and the amount which he invested in buying shares of each company.
Answer: Let the person's total savings be Rs.x. He invests 20% of x in company A, 30% of x in company B, and 25% of x in company C. This gives investments of Rs.x/5, Rs.3x/10, and Rs.x/4 respectively. Since the shares are bought at par, the nominal value equals the market value. The annual dividend from company A is (x/5) × (10/100) = Rs.x/50. The annual dividend from company B is (3x/10) × (12/100) = Rs.9x/250. The annual dividend from company C is (x/4) × (15/100) = Rs.3x/80. The total dividend is x/50 + 9x/250 + 3x/80 = 4675. Finding a common denominator (2000): (40x + 72x + 75x)/2000 = 4675, so 187x/2000 = 4675, giving x = 50000. Therefore, his savings are Rs.50000, with Rs.10000 invested in company A, Rs.15000 in company B, and Rs.12500 in company C.
In simple words: A man saves Rs.50000 and splits it across three companies. He puts Rs.10000 in company A (earning 10% dividend), Rs.15000 in company B (earning 12%), and Rs.12500 in company C (earning 15%). All together, these give him Rs.4675 in yearly dividend income.

Exam Tip: When setting up the total dividend equation, convert all fractions to a common denominator before adding; this reduces arithmetic errors and makes the final equation cleaner.

Question 10. Virat and Dhoni invest Rs.36000 each in buying shares of two companies. Virat buys 15% Rs.40 shares at a discount of 20%, while Dhoni buys Rs.75 shares at a premium of 20%. If both receive equal dividends at the end of the year, find the rate percent of the dividend declared by Dhoni's company.
Answer: Virat invests Rs.36000 in shares with nominal value Rs.40. At a 20% discount, the market value is Rs.40 - Rs.8 = Rs.32 per share. The number of shares Virat buys is 36000/32 = 1125. His annual dividend is 1125 × (15/100) × 40 = Rs.6750. Dhoni also invests Rs.36000 in shares with nominal value Rs.75. At a 20% premium, the market value is Rs.75 + Rs.15 = Rs.90 per share. The number of shares Dhoni buys is 36000/90 = 400. Let the dividend rate declared by Dhoni's company be r%. His annual dividend is 400 × (r/100) × 75 = Rs.300r. Since both receive equal dividends: 300r = 6750, so r = 22.5. Therefore, the rate of dividend declared by Dhoni's company is 22.5%.
In simple words: Virat and Dhoni each put Rs.36000 into different shares. Virat gets Rs.6750 in yearly dividend. Dhoni must get the same amount, which means his company must declare a dividend rate of 22.5%.

Exam Tip: Set both annual dividends equal and solve for the unknown dividend rate; remember that the annual dividend depends on the number of shares held (which depends on market price) multiplied by the dividend rate and nominal value.

Question 11. A man invests Rs.36,000 in 15% Rs.100 shares at Rs.120, when the market value of this shares rose to Rs.200, he sold some shares to purchase a laptop worth Rs.40,000. Calculate: (i) the number of shares he still holds (ii) the dividend he will get on these remaining shares.
Answer:
(i) The man's initial investment is Rs.36000 at a market price of Rs.120 per share. The number of shares purchased is 36000/120 = 300. When the market value rises to Rs.200, the man sells shares to raise Rs.40000 for the laptop. The number of shares sold is 40000/200 = 200. The remaining shares held are 300 - 200 = 100.
(ii) The annual dividend on 100 shares is calculated as: 100 × (15/100) × 100 = Rs.1500. Therefore, the man holds 100 shares and receives Rs.1500 as annual dividend on the remaining shares.
In simple words: The man starts with 300 shares. He sells 200 of them at Rs.200 each to buy a laptop. He keeps 100 shares, which earn him Rs.1500 every year in dividend.

Exam Tip: Always carefully track the number of shares at each stage (initial purchase, then sold, then remaining); use the correct market price for each transaction, as this changes the number of shares that can be bought or sold with a given amount of money.