14-09-2021 Answers

1. The monthly salary of X, Y, Z is in the proportion of 2 : 3 : 5. If Z’s monthly salary is Rs. 1500 more than that of X, find Y’s annual salary ?

Answer: Rs. 18000

Solution: Let the monthly salary of X, Y, Z be 2x, 3x, and 5x respectively.

5x - 2x = 1500, x = 500

Y’s monthly salary = 1500

Y’s annual salary = (12 * 1500) 18000

2. Rs. 980 is divided among Ram, Sam and Gopal. The share of Ram is 2/5 th of the combined share of Sam and Gopal. Find Ram’s share.

Answer: Rs. 280

Solution: Ram : (Sam + Gopal) = 2 : 5

Ram’s share = (980 * (2 / 7) = 280

3. Out of the ratios 17 : 15, 15 : 23, 24 : 25 and 21 : 29, find the largest one

Answer: 17:15

Solution: Only in 17/15, numerator is more than denominator and hence the largest.

4. In a class the number of boys is more than number of girls by 15% of the total strength. Find the ratio of boys to girls.

Answer: 23:17

Solution: Let the number of boys and girls be x and y respectively.

Then, (x - y) = 15% of (x + y)

x - y   = (15 / 100) * (x + y)

17x = 23y

x / y = 23 / 17

5. Two numbers are in the ratio 3 : 5. If each number is increased by 10, the ratio becomes 5 : 7.

Find the numbers.

Answer: 15, 25

Solution: Let the numbers be 3x and 5x

Then   (3x + 10) / (5x + 10) = 5 / 7,  x = 5

6. Fifteen bananas and seven mangoes cost as much as ten bananas and nine mangoes. What is the ratio of the cost of one banana to a mango?

Answer: 2:5

Solution: Let cost of one banana be b and a mango be m.

15b + 7m = 10b + 9m, 5b = 2m, b/m = 2/5

7. The cost of making an article is divided among materials, labour and overheads in the ratio of 3 : 4 : 1. If the materials cost of Rs.72, find the cost of the article.

Answer: Rs.192

Solution: If material cost Rs. 3, the cost of the article = (3 + 4 + 1) = Rs. 8

If the material cost Rs 72, the cost of the article = (8 / 3) * 72 = 192

8. Rs. 53 is divided among X, Y and Z in such a way that X gets Rs. 7 more than what Y gets and Y gets Rs. 8 more than what Z gets. Find the ratio of their shares.

Answer: 25:18: 10

Solution: Suppose Z gets a

Then, Y gets (a + 8) and X gets (a + 8 + 7)

a + a + 8 + a + 15 = 53, a = 10

X : Y : Z = 25 : 18 : 10

9. What must be added to each term of the ratio 7 : 13 so that the ratio becomes 4 :5 ?

Answer: 17

Solution: (7 + x) / (13 + x) = 4 /5 = 17

10. In a mixture of 60 litres, the ratio of milk and water is 3 : 2. What amount of water must be added to make the ratio 1 : 2 ?

Answer: 48 litres

Solution: Milk = (60 * (3 / 5) = 36

Water = 60 - 36 = 24

36 / (24 + x) = 1 / 2

x = 48

11. If one-third of X, one-fourth of Y and one-fifth of Z are equal, find the ratio between X, Y and Z.

Answer: 3:4:5

Solution: (1 / 3)X = (1 / 4)Y = (1 / 5)Z = x

X = 3x, Y = 4x, Z = 5x. X : Y : Z = 3 : 4 : 5

12. If 20% of A is the same as 40% of B, find A : B.

Answer: 2:1

Solution: 20 % of A = 40% of B

20A / 100 = 40B / 100. A / B = 40/20 = 2 : 1

13. 6 men, 8 women, 6 children complete a job for a sum of Rs. 1050. If their individual wages are in the ratio 4 : 3 : 2, find the total money earned by the children.

Answer: 210

Solution: Ratio of wages of 6 men, 8 women and 6 children = 6 * 4 : 8 * 3 : 6 * 2 = 2 : 2 : 1

Total money earned by children = (1050 * 1 / 5) = 210

14. The ratio of two numbers is 5 : 4 and their sum is 540. Find the greater of the two numbers.

Answer: 300

Solution: Greater number = 540 * (5 / (5+4)) = 300

15. The boys in three classes are in the ratio 2 : 3 : 5. If 20 boys are increased in each class,  the  ratio changes to 4 : 5 : 7. Find the total number of boys before the increase.

Answer: 100

Solution: Let the number of boys be 2x, 3x and 5x

(2x + 20) : (3x + 20) : (5x + 20) = 4 : 5 : 7

Solving we get x = 10. Total number of boys before increase = 2x+3x+5x = 10x = 100