CBSE Class 10 Mathematics Pair of Linear Equations in Two Variables VBQs Set 08

Question. The sum of the digits of a two digit number is 8 and the difference between the number and that formed by reversing the digits is 18. Find the number.
Answer: 53

Question. A train covered a certain distance at a uniform speed. If the train would have been 6 km/hr. faster, it would have taken 4 hours less than the scheduled time. And if the train were slower by 6 km/hr., it would have taken 6 hours more than the scheduled time. Find the length of the journey.
Answer: 720 km

Question. Ratio between the girls and boys in a class of 40 students is 2 : 3. Five new students joined the class. How many of them must be boys so that the ratio between girls and boys becomes 4 : 5?
Answer: 1

Question. If you travel by an autorickshaw the fare for the first kilometre is different from the rate per km for the remaining distance. The total fare for a distance of 20 km is Rs. 37.70 and that for a distance of 26 km is Rs. 48.50. Find the auto fare for the first kilometre and for each successive kilometre.
Answer: Rs. 3.50, Rs. 1.80

Question. One kilogram of tea and 4 kg of sugar together cost Rs. 220. If the price of sugar increases by 50% and the price of tea increases by 10% the cost would be Rs. 266. Find the original cost per kilogram of each.
Answer: Rs. 160, Rs. 15

Question. A man bought 4 horses and 9 cows for Rs. 1340. He sells the horses at a profit of 10% and the cows at a profit of 20% and his whole gain is Rs. 188. What price did he pay for the horse?
Answer: Rs. 200

Question. The largest angle of a triangle is equal to the sum of the other two angles. The smallest angle is 1/4 of the largest angle. Find the angles of the triangle.
Answer: \( 22\frac{1}{2}^{\circ}, 67\frac{1}{2}^{\circ} \) and \( (90)^{\circ} \)

Question. A man when asked how many hens and buffaloes he has told that his animals have 120 eyes and 180 legs. How many hens and buffaloes has he?
Answer: Buffaloes = 30, Hens = 30

Question. The sum of a two digit number and the number obtained by reversing the order of its digits is 121 and the two digits differ by 3. Find the number.
Answer: 74 or 47

Question. A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Bombay to Ahmedabad costs Rs. 216 and one full and one half reserved first class tickets cost Rs. 327. What is the basic first class full fare and what is the reservation charge?
Answer: Full basic fare = Rs. 210, Reservation charges = Rs. 6

Question. A fraction becomes 4/5 if 1 is added to both numerator and denominator. If however 5 is subtracted from both numerator and denominator, the fraction becomes 1/2. What is the fraction?
Answer: \( \frac{7}{9} \)

Question. Seven times a two digit number is equal to four times the number obtained by reversing the order of digits, and the sum of the digits of the number is 3. Find the number.
Answer: 12

Question. A two digit number is obtained by either multiplying sum of the digits by 8 and adding 1 or by multiplying the difference of the digits by 13 and adding 2. Find the number.
Answer: 41

Question. 3 chairs and 2 tables cost Rs. 700 and 5 chairs and 3 tables cost Rs. 1100. What is the cost of 2 chairs and 2 tables?
Answer: Rs. 82

Question. Points A and B are 70 km apart on a highway. A car starts from A and another car starts from B at the same time. If they travel in the same direction, they meet in 7 hrs. but if they travel towards each other they meet, in one hour. What are their speeds?
Answer: 30 km/hr, 40 km/hr

Question. A man starts his job with a certain monthly salary and earns a fixed increment every year. If his salary was Rs. 1500 after 4 years of service and Rs. 1800 after 10 years of service what was his starting salary and what is the annual increment?
Answer: Rs. 1300 and Rs. 50

Question. A train covered a certain distance at a uniform speed. If the train would have been 6 km/hr. faster it would have taken 4 hrs less than the scheduled time. And if the train were slower by 6 km/hr., it would have taken 6 hrs more than the scheduled time. Find the length of the journey.
Answer: 720 km

Question. A villager went to a hotel in a town with his big family. They consumed 23 idlies, 18 pooris, 7 dosas and 19 vadas. The bill come to Rs. 108. On next day, they consumed 34 idlies, 8 vadas, 22 pooris and 7 dosas. The bill came to Rs. 114. If an idli costs the same as a vada, what is the cost of one poori?
Answer: Rs. 1.50

Question. A man walks a certain distance with certain speed. If he walks 1/2 km/hr. faster, he takes 1 hr. less. But if he walks 1 km/hr. slower, he takes 3 more hours. Find the distance covered by the man and his original rate of walking.
Answer: Distance = 36 km, speed = 4 km/hr

Question. The incomes of X and Y are in the ratio of 8 : 7 and their expenditures are in the ratio 19 : 16. If each saves Rs. 1250, find their incomes.
Answer: Rs. 6000, Rs. 5250

Question. A and B each has a certain number of mangoes. A says to B, "if you give 30 of your mangoes I will have twice as many as left with you." B replies "if you give me 10, I will have thrice as many as left with you". How many mangoes does each have?
Answer: A = 34, B = 62

Question. A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Find the speed of the boat in still water and the speed of the stream.
Answer: 10 km/hr

Question. A two-digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3. Find the number.
Answer: 83

Question. A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, thereby, getting a sum Rs. 1008. If she had sold the saree at 10% profit and the sweater at 8% discount, she would have got Rs. 1028. Find the cost price of the saree and the list price (price before discount) of the sweater.
Answer: Rs. 600

Question. Susan invested certain amount of money in two schemes A and B, which offer interest at the rate of 8% per annum and 9% per annum, respectively. She received Rs. 1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would have received Rs. 20 more as annual interest. How much money did she invest in each scheme?
Answer: Rs. 12000 with scheme A and Rs. 10,000

Question. Vijay had some bananas, and he divided them into two lots A and B. He sold the first lot at the rate of Rs. 2 for 3 bananas and the second lot at the rate of Rs. 1 per banana, and got a total of Rs. 400. If he had sold the first lot at the rate of Rs. 1 per banana, and the second lot at the rate of Rs. 4 for 5 bananas, his total collection would have been Rs. 460. Find the total number of bananas he had.
Answer: 500

Question. The area of a rectangle gets reduced by 80 sq. units if its length is reduced by 5 units and the breadth is increased by 2 units. If we increase the length by 10 units and decrease the breadth by 5 units, the area is increased by 50 sq. units. Find the length and breadth of the rectangle.
Answer: Length = 40 units, Breadth = 30 units

Question. The total expenditure per month of a household consists of a fixed rent of the house and mess charges depending upon the number of people sharing the house. The total monthly expenditure is Rs. 3900 for 2 people and Rs. 7500 for 5 people. Find the rent of the house and the mess charges per head per month.
Answer: Rs. 1500 and Rs. 1200

Question. A man travels 600 km partly by train and partly by car. If he covers 400 km by train and the rest by car, it takes him 6 hours and 30 minutes. But, if he travels 200 km by train and the rest by car, he takes an hour longer. Find the speed of the train and that of the car.
Answer: 100 km/hr, 80 km/hr

Question. A train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/hr from its usual speed. Find the usual speed of the train.
Answer: 25 km/hr

Question. A chemist has one solution which is 40% acid and another which is 20% acid. How much of each solution should the chemist mix to get 10 L (litre) of a solution which is 25% acid?
Answer: \( \frac{5}{2} \) liters of first and \( \frac{15}{2} \) liters of second

Question. One hundred and fifty students are admitted to a school. They are distributed over three sections A, B and C. If 6 students are shifted from section A to section C, the two sections will have equal number of students. If 4 times of students of C exceeds the number of students of section A by the number of students in section B, find the number of students in the three sections.
Answer: (42, 78 and 30)

Question. The distance between two places A and B is 300 metres. Rohan starts running from A towards B while Deepak starts running from B towards A. They meet after 4 minutes. Had Rohan doubled his speed and Deepak reduced his by 50%, they would have met one minute earlier. Find their respective speeds.
Answer: \( 20\frac{5}{6} \) km/hr and \( 4\frac{1}{6} \) km/hr

Question. Mr John has a son and a daughter, the son being 4 years older than the daughter. Five years ago, the age of Mr John was 23 years more than the sum of the ages of his son and daughter. After 18 years from now, the age of Mr John will be seventeen times the difference of ages of his son and daughter. Find their present ages.
Answer: 50 years, 18 years, 14 years

Question. A dishonest milkman has one bucket of milk of 80% purity. He has another bucket milk of 60% purity. How much milk of each kind should he mix to supply 20 litres of milk of 75% purity?
Answer: 15 liters and 5 liters

Question. A milkman has a smaller drum half full of milk and a larger one of twice, the capacity of the smaller one with 1/4 full of milk. He adds water to the two drums so that both of them are full. The milk in both the drams are emptied into a tub. What is the fraction of the milk in the contents of the type?
Answer: Fraction = \( \frac{1}{3} \)

Question. If two liquids are mixed in the ratio 4 : 3, a mixture is obtained weighing 1.04 g per c.c.; while if they are mixed in the ratio 6 : 4, the resulting mixture weighs 1.05 per c.c. Find the weight of a c.c. of each of original liquids.
Answer: \( x = 1.19, y = 0.86 \)

Question. A cyclist after riding a certain distance stopped for half an hour to repair his machine after which he completes the whole journey of 30 km at half speed in 5 hours. If breakdown had occurred 10 km further off, he would have done the whole journey in 4 hrs. Find where the breakdown occurred and his original speed.
Answer: Original speed = 10km/hr, The breakdown occurred after 15 km from initial position.

Question. A train overtakes two persons who are walking in the same direction in which the train is going, at the speed of 2 kmph and 4 kmph passess them completely in 9 and 10 seconds respectively. Find the length and speed of the train.
Answer: 50 m and \( \frac{50}{9} \) m/second

Question. A number consists of three digits, of which the middle one is 0. If the left hand and right hand digits be interchanged the number is increased by 198. If the left hand digit be halved and the middle and the right hand digits be interchanged, the number is diminished by 228. Find the number.
Answer: 608

Question. A man wished to give Rs. 12 to each person and found that he fell short of Rs. 6 when he wanted to give all the persons present. He, therefore, distributed Rs. 9 to each person and found that Rs. 9 were left over. How much money did he have and how many persons were there?
Answer: 54

Question. While covering a distance of 30 km, Ajeet takes 2 hours more than Amit. If Ajeet doubles his speed he would take 1 hour less than Amit, find their ratio of walking.
Answer: Speed of Ajit = 5km/hr and speed of Amit = 7.5 km/hr

Question. 2 kg of tea and 3 kg of sugar together cost Rs. 205. The price of tea rises by 20% and that of sugar by 10%. The same quantity of tea and sugar now cost Rs. 241.50. Find the original price of tea and sugar.
Answer: Tea = Rs. 80 per kg, Sugar = Rs. 15 per kg

Question. When 6 new boys were admitted and 6 girls were left from the class the % of boys in the class increased from 60% to 75%. Find the original number of boys and girls in the class.
Answer: Boys 24, Girls = 16

Question. When the son will be as old as the father today their ages will add up to 126 years. When the lather was as old as the son is today, their ages added up to 38 years. Find their present ages.
Answer: Son's age = 30 years, Father's age = 52 years

Question. A lady has 25 P and 50 P coins in her purse. If in all she has 40 coins totalling Rs. 12.50, find the number of coins of each type she has.
Answer: 25 paise coins = 30 and 50 paise coins = 10

Question. In an examination, the number of those that passed and the number of those that failed were in the ratio 3 : 1. Had 8 more appeared, and 6 less passed, the ratio of passes to failures would have been 2 : 1. Find how many appeared?
Answer: 136

Question. A boy walks to a picnic spot from his house in 6 hours, but he can travel the same distance on his cycle in 2 hours. If his average cycling speed is 7 kilometres per hour faster than his average walking speed, find his average walking speed and his average cycling speed.
Answer: 3.5 km/hr, 10.5 km/hr

Question. The width of a rectangular room is 4/7 of its length \( x \) and its perimeter is \( y \). Write an equation connecting \( x \) and \( y \). Find the length of the room when the perimeter is 4400 cm.
Answer: 1400 cm

Question. A person invested some amount at the rate of 10% simple interest and some other amount at the rate of 12% simple interest. He received yearly interest of Rs. 130. But if he had interchanged the amounts invested, he would have received Rs. 4 more as interest. How much amount did he invest at different rates?
Answer: At 12% amount is Rs. 500 and at 10% amount is Rs. 700