Selina Concise Solutions for ICSE Class 7 Mathematics Chapter 10 Simple Interest

Simple Interest

Points to Remember

• Simple Interest: Simple Interest (or \(\text{S.I.}\)) is calculated using the formula:
  \(\text{Simple Interest} = \frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100}\)
• Formulas derived from Simple Interest:
  • Principal (\(P\)) = \(\frac{\text{S.I.} \times 100}{R \times T}\)
  • Rate (\(R\)) = \(\frac{\text{S.I.} \times 100}{P \times T}\)
  • Time (\(T\)) = \(\frac{\text{S.I.} \times 100}{P \times R}\)
• Amount: The total amount (\(A\)) is the sum of the Principal and the Simple Interest:
  \(\text{Amount} = \text{Principal} + \text{Simple Interest}\)
  
  \(\implies A = P + \text{S.I.} = P + \frac{P \times R \times T}{100}\)

Question 1. Find the S.I. and amount on :
(i) Rs. 150 for 4 years at 5% per year.
(ii) Rs. 350 for 3\(\frac{1}{2}\) years at 8% p.a.
(iii) Rs. 620 for 4 months at 8 p. per rupee per month.
(iv) Rs. 3,380 for 30 months at 4\(\frac{1}{2}\)% p.a.
(v) Rs. 600 from July 12 to Dec. 5 at 10% p.a.
(vi) Rs. 850 from 10th March to 3rd August at 2\(\frac{1}{2}\)% p.a.
(vii) Rs. 225 for 3 years 9 months at 16% p.a.
Answer:
(i) Here, the values are:
Principal (\(P\)) = Rs. 150
Rate of interest (\(R\)) = 5% each year
Time period (\(T\)) = 4 years
Now, let us calculate the Simple Interest (S.I.):
\(\text{S.I.} = \frac{P \times R \times T}{100}\)

\(\implies \text{S.I.} = \frac{150 \times 5 \times 4}{100} = \text{Rs. 30}\)
To find the final amount (\(A\)), we add the interest to the principal:
\(A = P + \text{S.I.}\)

\(\implies A = \text{Rs. 150} + \text{Rs. 30} = \text{Rs. 180}\)

(ii) For this part, we have:
Principal (\(P\)) = Rs. 350
Rate of interest (\(R\)) = 8% per year
Time period (\(T\)) = 3\(\frac{1}{2}\) years = \(\frac{7}{2}\) years
Using the formula for Simple Interest:
\(\text{S.I.} = \frac{P \times R \times T}{100}\)

\(\implies \text{S.I.} = \frac{350 \times 8 \times 7}{100 \times 2} = \text{Rs. 98}\)
Now, let us find the total amount:
\(A = P + \text{S.I.}\)

\(\implies A = \text{Rs. 350} + \text{Rs. 98} = \text{Rs. 448}\)

(iii) Here, we have:
Principal (\(P\)) = Rs. 620
Rate (\(R\)) = 8 paise per rupee per month = 8% per month
Time period (\(T\)) = 4 months
Since both the rate and time are in months, we can calculate S.I. directly:
\(\text{S.I.} = \frac{P \times R \times T}{100}\)

\(\implies \text{S.I.} = \frac{620 \times 8 \times 4}{100} = \frac{19840}{100} = \text{Rs. 198.40}\)
Next, we calculate the total amount:
\(A = P + \text{S.I.}\)

\(\implies A = \text{Rs. 620} + \text{Rs. 198.40} = \text{Rs. 818.40}\)

(iv) For this part:
Principal (\(P\)) = Rs. 3,380
Rate (\(R\)) = 4\(\frac{1}{2}\)% per year = \(\frac{9}{2}\)% per year
Time period (\(T\)) = 30 months = \(\frac{30}{12}\) years
Now, we find the Simple Interest:
\(\text{S.I.} = \frac{P \times R \times T}{100}\)

\(\implies \text{S.I.} = \frac{3380 \times 9 \times 30}{100 \times 2 \times 12} = \text{Rs. } \frac{1521}{4} = \text{Rs. 380.25}\)
To get the total amount:
\(A = P + \text{S.I.}\)

\(\implies A = \text{Rs. 3,380} + \text{Rs. 380.25} = \text{Rs. 3,760.25}\)

(v) We have:
Principal (\(P\)) = Rs. 600
Rate (\(R\)) = 10% per year
Let us count the number of days from July 12 to December 5:
July (31 - 12) = 19 days
August = 31 days
September = 30 days
October = 31 days
November = 30 days
December = 5 days
Total days = 146 days
Time period in years (\(T\)) = \(\frac{146}{365}\) years = \(\frac{2}{5}\) years
Calculating the Simple Interest:
\(\text{S.I.} = \frac{P \times R \times T}{100}\)

\(\implies \text{S.I.} = \frac{600 \times 10 \times 2}{100 \times 5} = \text{Rs. 24}\)
Calculating the total amount:
\(A = P + \text{S.I.}\)

\(\implies A = \text{Rs. 600} + \text{Rs. 24} = \text{Rs. 624}\)

(vi) We have:
Principal (\(P\)) = Rs. 850
Rate (\(R\)) = 2\(\frac{1}{2}\)% per year = \(\frac{5}{2}\)% per year
Let us count the number of days from March 10 to August 3:
March (31 - 10) = 21 days
April = 30 days
May = 31 days
June = 30 days
July = 31 days
August = 3 days
Total days = 146 days
Time period in years (\(T\)) = \(\frac{146}{365}\) years = \(\frac{2}{5}\) years
Now, calculating the Simple Interest:
\(\text{S.I.} = \frac{P \times R \times T}{100}\)

\(\implies \text{S.I.} = \frac{850 \times 5 \times 2}{100 \times 2 \times 5} = \frac{850}{100} = \text{Rs. 8.50}\)
Now, the total amount:
\(A = P + \text{S.I.}\)

\(\implies A = \text{Rs. 850} + \text{Rs. 8.50} = \text{Rs. 858.50}\)

(vii) We have:
Principal (\(P\)) = Rs. 225
Rate (\(R\)) = 16% per year
Time period (\(T\)) = 3 years 9 months = 3\(\frac{9}{12}\) years = 3\(\frac{3}{4}\) years = \(\frac{15}{4}\) years
Let us find the Simple Interest:
\(\text{S.I.} = \frac{P \times R \times T}{100}\)

\(\implies \text{S.I.} = \frac{225 \times 16 \times 15}{100 \times 4} = \text{Rs. 135}\)
To get the total amount:
\(A = P + \text{S.I.}\)

\(\implies A = \text{Rs. 225} + \text{Rs. 135} = \text{Rs. 360}\)
In simple words: Simple interest is calculated by multiplying the principal, rate, and time, then dividing by 100. Adding this interest back to the starting money gives the total amount.

Exam Tip: When counting days for interest calculation, remember that the day money is deposited is usually excluded, but the day of withdrawal is included. Always convert days to years by dividing by 365.

Question 2. On what sum of money does the S.I. for 10 years at 5% become Rs. 1,600 ?
Answer: We are given the following values:
Simple Interest (\(\text{S.I.}\)) = Rs. 1,600
Rate of interest (\(R\)) = 5% per year
Time period (\(T\)) = 10 years
We need to find the principal (\(P\)). Using the formula for principal:
\(P = \frac{\text{S.I.} \times 100}{R \times T}\)

\(\implies P = \frac{1600 \times 100}{5 \times 10} = \text{Rs. 3,200}\)
So, the sum of money is Rs. 3,200.
In simple words: To find the starting money, we multiply the interest by 100 and then divide it by the rate times the time.

Exam Tip: Be sure to write the formula clearly before substituting values, as showing the correct formula usually earns step-marks.

Question 3. Find the time in which Rs. 2,000 will amount to Rs. 2,330 at 11% p.a. ?
Answer: We are given:
Principal (\(P\)) = Rs. 2,000
Total Amount (\(A\)) = Rs. 2,330
Rate of interest (\(R\)) = 11% per year
First, we calculate the Simple Interest (\(\text{S.I.}\)):
\(\text{S.I.} = A - P\)

\(\implies \text{S.I.} = \text{Rs. 2,330} - \text{Rs. 2,000} = \text{Rs. 330}\)
Now, we can find the time (\(T\)) using the formula:
\(T = \frac{\text{S.I.} \times 100}{P \times R}\)

\(\implies T = \frac{330 \times 100}{2000 \times 11} = \frac{3}{2}\text{ years} = 1\frac{1}{2}\text{ years}\)
Thus, the required time is 1\(\frac{1}{2}\) years.
In simple words: First subtract the starting amount from the final amount to find the interest. Then divide this interest multiplied by 100 by the starting amount times the rate to get the time.

Exam Tip: Don't forget to convert improper fractions like \(\frac{3}{2}\) into a mixed fraction like 1\(\frac{1}{2}\) years for the final answer.

Question 4. In what time will a sum of money double it self at 8% p.a ?
Answer: Let us assume the initial principal (\(P\)) is Rs. 100.
Since the sum doubles itself, the final amount (\(A\)) will be:
\(A = \text{Rs. 100} \times 2 = \text{Rs. 200}\)
Now, let us find the Simple Interest (\(\text{S.I.}\)):
\(\text{S.I.} = A - P\)

\(\implies \text{S.I.} = \text{Rs. 200} - \text{Rs. 100} = \text{Rs. 100}\)
The interest rate (\(R\)) is given as 8% per year.
Now, let us calculate the time (\(T\)):
\(T = \frac{\text{S.I.} \times 100}{P \times R}\)

\(\implies T = \frac{100 \times 100}{100 \times 8} = \frac{25}{2}\text{ years} = 12\frac{1}{2}\text{ years}\)
So, the money will double in 12\(\frac{1}{2}\) years.
In simple words: If you assume the starting money is Rs. 100, doubling means it becomes Rs. 200. This means you need Rs. 100 in interest, which will take twelve and a half years at an 8% rate.

Exam Tip: When a question does not give a specific sum of money, assuming the principal to be Rs. 100 is a very helpful technique to simplify the calculation.

Question 5. In how many years will Rs. 870 amount to Rs. 1,044, the rate of interest being 2\(\frac{1}{2}\)% p.a ?
Answer: Here, we are given:
Principal (\(P\)) = Rs. 870
Total Amount (\(A\)) = Rs. 1,044
First, find the Simple Interest (\(\text{S.I.}\)):
\(\text{S.I.} = A - P\)

\(\implies \text{S.I.} = \text{Rs. 1,044} - \text{Rs. 870} = \text{Rs. 174}\)
The interest rate (\(R\)) is:
\(R = 2\frac{1}{2}\%\text{ p.a.} = \frac{5}{2}\%\text{ p.a.}\)
Now, we calculate the time (\(T\)) using the formula:
\(T = \frac{\text{S.I.} \times 100}{P \times R}\)

\(\implies T = \frac{174 \times 100 \times 2}{870 \times 5} = 8\text{ years}\)
So, it will take 8 years for the sum to reach Rs. 1,044.
In simple words: Find the interest by subtracting Rs. 870 from Rs. 1,044. Then calculate the time using the standard time formula.

Exam Tip: Be careful when simplifying fractions in the denominator. A rate like \(\frac{5}{2}\)% puts 5 in the denominator and moves 2 up to the numerator as a multiplier.

Question 6. Find the rate percent if the S.I. on Rs. 275 is 2 years is Rs. 22.
Answer: We are given:
Principal (\(P\)) = Rs. 275
Simple Interest (\(\text{S.I.}\)) = Rs. 22
Time period (\(T\)) = 2 years
Now, we calculate the rate of interest (\(R\)):
\(R = \frac{\text{S.I.} \times 100}{P \times T}\)

\(\implies R = \frac{22 \times 100}{275 \times 2} = 4\%\text{ p.a.}\)
Therefore, the rate of interest is 4% per year.
In simple words: To find the interest rate, we divide the interest times 100 by the starting money times the number of years.

Exam Tip: Double check your division. Here, 22 times 100 is 2200, and 275 times 2 is 550, so dividing 2200 by 550 gives exactly 4%.

Question 7. Find the sum which will amount to Rs. 700 in 5 years at 8% rate p.a.
Answer: We have the following given values:
Total Amount (\(A\)) = Rs. 700
Rate of interest (\(R\)) = 8% per year
Time period (\(T\)) = 5 years
Let us assume the starting principal (\(P\)) is Rs. 100.
Under this assumption, the Simple Interest (\(\text{S.I.}\)) would be:
\(\text{S.I.} = \frac{P \times R \times T}{100}\)

\(\implies \text{S.I.} = \frac{100 \times 8 \times 5}{100} = \text{Rs. 40}\)
So, the total amount under our assumption would be:
\(A = P + \text{S.I.} = \text{Rs. 100} + \text{Rs. 40} = \text{Rs. 140}\)
Now, we can use a unitary method to find the actual principal:
If the final amount is Rs. 140, the principal is Rs. 100.
Therefore, if the actual amount is Rs. 700, the actual principal is:
\(P = \text{Rs. } \frac{100 \times 700}{140} = \text{Rs. 500}\)
Thus, the starting sum of money is Rs. 500.
In simple words: If we assume the starting money is Rs. 100, it would grow to Rs. 140 in five years. Since the real amount is Rs. 700 (which is 5 times larger), the real starting money must also be 5 times larger, which is Rs. 500.

Exam Tip: You can also solve this using the direct formula \(P = \frac{A \times 100}{100 + (R \times T)}\). Both methods are correct and yield the same result.

Question 8. What is the rate of interest, if Rs. 3,750 amounts to Rs. 4,650 in 4 years ?
Answer: We are given:
Principal (\(P\)) = Rs. 3,750
Total Amount (\(A\)) = Rs. 4,650
Time period (\(T\)) = 4 years
First, find the Simple Interest (\(\text{S.I.}\)):
\(\text{S.I.} = A - P\)

\(\implies \text{S.I.} = \text{Rs. 4,650} - \text{Rs. 3,750} = \text{Rs. 900}\)
Now, we find the rate of interest (\(R\)):
\(R = \frac{\text{S.I.} \times 100}{P \times T}\)

\(\implies R = \frac{900 \times 100}{3750 \times 4} = 6\%\text{ p.a.}\)
Hence, the rate of interest is 6% per year.
In simple words: First subtract the starting money from the final money to see that the interest earned is Rs. 900. Then use the rate formula to find that this equals 6% per year.

Exam Tip: Be careful with zero-cancellations in fractions. Simplifying \(\frac{90000}{15000}\) directly gives 6.

Question 9. In 4 years, Rs. 6,000 amount to Rs. 8,000. In what time will Rs. 525 amount to Rs. 700 at the same rate ?
Answer: Let us solve this in two steps:

First Case:
Principal (\(P_1\)) = Rs. 6,000
Total Amount (\(A_1\)) = Rs. 8,000
Time (\(T_1\)) = 4 years
First, we calculate the interest earned:
\(\text{S.I.}_1 = A_1 - P_1 = \text{Rs. 8,000} - \text{Rs. 6,000} = \text{Rs. 2,000}\)
Next, we calculate the rate of interest (\(R\)):
\(R = \frac{\text{S.I.}_1 \times 100}{P_1 \times T_1}\)

\(\implies R = \frac{2000 \times 100}{6000 \times 4} = \frac{25}{3}\%\text{ per year}\)

Second Case:
Principal (\(P_2\)) = Rs. 525
Total Amount (\(A_2\)) = Rs. 700
Rate of interest (\(R\)) = \(\frac{25}{3}\)% per year
First, we find the interest earned in this case:
\(\text{S.I.}_2 = A_2 - P_2 = \text{Rs. 700} - \text{Rs. 525} = \text{Rs. 175}\)
Now, we calculate the time (\(T_2\)):
\(T_2 = \frac{\text{S.I.}_2 \times 100}{P_2 \times R}\)

\(\implies T_2 = \frac{175 \times 100 \times 3}{525 \times 25} = 4\text{ years}\)
Thus, the time required is 4 years.
In simple words: First find the interest rate from the first case, which is \(\frac{25}{3}\)%. Then apply this interest rate to the second case to find that the time needed is 4 years.

Exam Tip: Keep the rate as a fraction \(\frac{25}{3}\)% instead of writing it as a recurring decimal. This makes it much easier to cancel numbers and simplify in the second step.

Question 10. The interest on a sum of money at the end of 2\(\frac{1}{2}\) years is \(\frac{4}{5}\) of the sum. What is the rate percent ?
Answer: Let us assume the starting principal (\(P\)) is Rs. 100.
According to the given condition, the Simple Interest (\(\text{S.I.}\)) is \(\frac{4}{5}\) of the principal:
\(\text{S.I.} = \text{Rs. 100} \times \frac{4}{5} = \text{Rs. 80}\)
The time period (\(T\)) is:
\(T = 2\frac{1}{2}\text{ years} = \frac{5}{2}\text{ years}\)
Now, we calculate the rate percent (\(R\)):
\(R = \frac{\text{S.I.} \times 100}{P \times T}\)

\(\implies R = \frac{80 \times 100 \times 2}{100 \times 5} = 32\%\text{ p.a.}\)
Therefore, the rate percent is 32% per annum.
In simple words: If you start with Rs. 100, the interest is Rs. 80. Over two and a half years, this interest matches a rate of 32% per year.

Exam Tip: Be systematic when converting words into algebraic expressions. "Interest is \(\frac{4}{5}\) of the sum" directly means \(\text{S.I.} = \frac{4}{5} \times P\).

Question 11. What sum of money lent out at 5% for 3 years will produce the same interest as Rs. 900 lent out at 4% for 5 years ?
Answer: We can solve this by looking at the two cases:

Second Case:
Principal (\(P\)) = Rs. 900
Rate (\(R\)) = 4% per year
Time (\(T\)) = 5 years
Now, let us calculate the Simple Interest generated in this case:
\(\text{S.I.} = \frac{P \times R \times T}{100}\)

\(\implies \text{S.I.} = \frac{900 \times 4 \times 5}{100} = \text{Rs. 180}\)

First Case:
According to the problem, this case produces the same interest:
Simple Interest (\(\text{S.I.}\)) = Rs. 180
Rate (\(R\)) = 5% per year
Time (\(T\)) = 3 years
We need to find the sum of money (Principal, \(P\)):
\(P = \frac{\text{S.I.} \times 100}{R \times T}\)

\(\implies P = \frac{180 \times 100}{5 \times 3} = \text{Rs. 1,200}\)
Thus, the required sum of money is Rs. 1,200.
In simple words: First work out the interest from the second part, which is Rs. 180. Since the first part must have this same interest, use it along with the 5% rate and 3-year term to find the starting sum of Rs. 1,200.

Exam Tip: When a question links two situations together, clearly label each part as "Case 1" and "Case 2" to make your steps easy for the examiner to follow.

Question 12. A sum of Rs. 1,780 become Rs. 2,136 in 4 years, Find :
(i) the rate of interest.
(ii) the sum that will become Rs. 810 in 7 years at the same rate of interest ?
Answer:
(i) First, we find the rate of interest using the given values:
Principal (\(P\)) = Rs. 1,780
Total Amount (\(A\)) = Rs. 2,136
Time (\(T\)) = 4 years
Let us calculate the interest earned first:
\(\text{S.I.} = A - P = \text{Rs. 2,136} - \text{Rs. 1,780} = \text{Rs. 356}\)
Now, let us find the rate (\(R\)):
\(R = \frac{\text{S.I.} \times 100}{P \times T}\)

\(\implies R = \frac{356 \times 100}{1780 \times 4} = 5\%\text{ p.a.}\)
So, the rate of interest is 5% per year.

(ii) Next, we find the starting sum that grows to Rs. 810 in 7 years at this same 5% interest rate:
Total Amount (\(A\)) = Rs. 810
Time (\(T\)) = 7 years
Rate (\(R\)) = 5% per year
Let us assume the starting principal (\(P\)) is Rs. 100.
Under this assumption, the Simple Interest (\(\text{S.I.}\)) would be:
\(\text{S.I.} = \frac{100 \times 5 \times 7}{100} = \text{Rs. 35}\)
This means the total amount would be:
\(A = P + \text{S.I.} = \text{Rs. 100} + \text{Rs. 35} = \text{Rs. 135}\)
Now, we use the unitary method:
If the final amount is Rs. 135, the principal is Rs. 100.
So, if the final amount is Rs. 810, the principal must be:
\(P = \text{Rs. } \frac{100 \times 810}{135} = \text{Rs. 600}\)
Thus, the required sum of money is Rs. 600.
In simple words: First find the interest rate from the first part, which is 5%. Then assume Rs. 100 as the principal for the second part, which grows to Rs. 135. Comparing this to the actual amount of Rs. 810 tells us the starting sum was Rs. 600.

Exam Tip: Be careful with sub-questions. Solving part (i) correctly is necessary because its result (the 5% rate) is used to solve part (ii).

Question 13. A sum amounts to Rs. 2,652 in 6 years at 5% p.a. simple interest. Find :
(i) the sum
(ii) the time in which the same sum will double itself at the same rate of interest.
Answer:
(i) First, let us find the starting sum (principal):
Total Amount (\(A\)) = Rs. 2,652
Time (\(T\)) = 6 years
Rate (\(R\)) = 5% per year
Let us assume the initial principal (\(P\)) is Rs. 100.
Using this assumption, the Simple Interest (\(\text{S.I.}\)) would be:
\(\text{S.I.} = \frac{100 \times 5 \times 6}{100} = \text{Rs. 30}\)
The total amount under this assumption is:
\(A = \text{Rs. 100} + \text{Rs. 30} = \text{Rs. 130}\)
Now, we use the unitary method:
If the total amount is Rs. 130, then the principal is Rs. 100.
So, if the actual total amount is Rs. 2,652, the actual principal is:
\(P = \text{Rs. } \frac{100 \times 2652}{130} = \text{Rs. 2,040}\)
Therefore, the sum is Rs. 2,040.

(ii) Next, we find the time in which this same sum (Rs. 2,040) will double itself at the 5% interest rate:
Since the sum doubles itself, let us assume the principal (\(P\)) is Rs. 100.
Then the total amount (\(A\)) will be:
\(A = \text{Rs. 100} \times 2 = \text{Rs. 200}\)
The interest required is:
\(\text{S.I.} = A - P = \text{Rs. 200} - \text{Rs. 100} = \text{Rs. 100}\)
The rate of interest (\(R\)) is 5% per year.
Now, we find the time (\(T\)):
\(T = \frac{\text{S.I.} \times 100}{P \times R}\)

\(\implies T = \frac{100 \times 100}{100 \times 5} = 20\text{ years}\)
Thus, the sum will double itself in 20 years.
In simple words: First assume a starting money of Rs. 100 to find that the real principal is Rs. 2,040. In the second part, doubling any sum at a 5% rate will always take 20 years.

Exam Tip: When calculating how long it takes for a sum to double, the actual value of the principal doesn't affect the final time, so you can simply use Rs. 100 for your calculations.

Question 14. P and Q invest Rs. 36,000 and Rs. 25,000 respectively at the same rate of interest per year. If at the end of 4 years, P gets Rs. 3,080 more interest than Q; find the rate of interest.
Answer: Let us denote the common rate of interest as \(x\%\) per annum.
We are given:
P's investment (\(P_1\)) = Rs. 36,000
Q's investment (\(P_2\)) = Rs. 25,000
Time period (\(T\)) = 4 years

Now, let us find the interest earned by P:
\(\text{Interest earned by P} = \frac{36000 \times x \times 4}{100} = \text{Rs. 1,440}x\)

Next, let us find the interest earned by Q:
\(\text{Interest earned by Q} = \frac{25000 \times x \times 4}{100} = \text{Rs. 1,000}x\)

The difference in the interest earned is:
\(\text{Difference} = \text{Rs. 1,440}x - \text{Rs. 1,000}x = \text{Rs. 440}x\)
According to the problem, this difference is Rs. 3,080:
\(440x = 3080\)

\(\implies x = \frac{3080}{440} = 7\%\)
Therefore, the rate of interest is 7% per annum.
In simple words: Represent the rate of interest as x. Find the interest for both P and Q, subtract them, and set this equal to the difference of Rs. 3,080 to solve for x.

Exam Tip: Be sure to clearly define your variable (like letting the rate be \(x\%\)) at the very beginning of your solution.

Question 15. A sum of money is lent for 5 years at R% simple interest per annum. If the interest earned be one-fourth of the money lent, find the value of R.
Answer: Let us assume the starting principal (\(P\)) is Rs. 100.
Since the interest earned is one-fourth of the principal, we have:
\(\text{Simple Interest (S.I.)} = \frac{1}{4} \times \text{Rs. 100} = \text{Rs. 25}\)
The time period (\(T\)) is 5 years.
Now, we calculate the rate of interest (\(R\)):
\(R = \frac{\text{S.I.} \times 100}{P \times T}\)

\(\implies R = \frac{25 \times 100}{100 \times 5} = 5\%\)
Thus, the value of \(R\) is 5.
In simple words: If you assume the starting sum is Rs. 100, the interest is Rs. 25. Over 5 years, this gives a rate of 5% each year.

Exam Tip: Always make sure to answer the specific question asked; here, write "the value of R is 5" because the question asks for "the value of R" where the rate is already defined as R%.

Question 16. The simple interest earned on a certain sum in 5 years is 30% of the sum. Find the rate of interest.
Answer: Let us assume the starting principal (\(P\)) is Rs. 100.
The Simple Interest (\(\text{S.I.}\)) is 30% of this principal:
\(\text{S.I.} = \frac{30}{100} \times \text{Rs. 100} = \text{Rs. 30}\)
The time period (\(T\)) is 5 years.
Now, we calculate the rate of interest (\(R\)):
\(R = \frac{\text{S.I.} \times 100}{P \times T}\)

\(\implies R = \frac{30 \times 100}{100 \times 5} = 6\%\text{ p.a.}\)
Therefore, the rate of interest is 6% per annum.
In simple words: If the principal is Rs. 100, the interest is Rs. 30. Over 5 years, that means you earn Rs. 6 every year, which is a 6% rate.

Exam Tip: Expressing percentages as fractions of 100 (like 30% of Rs. 100 being Rs. 30) makes it extremely easy to solve these problems without dealing with difficult decimals.