Maths made simpler with these sums

This article is in continuation to the last article focusing on the ratio and proportion topic. Here are some practice questions along with solutions

This article is in continuation to the last article focusing on the ratio and proportion topic. Here are some practice questions along with solutions on the ratio and proportion topic.

Four years ago, the ratio of A’s age to B’s age was 11 : 14 and four years later their age will be in the ratio 13 : 16. The present age of A is?

---

a) 42 years (b) 46 years c) 44 years d) 48 years

Ans: d

Solution: Let the age of A and B four years ago be 11x and 14x years respectively.
According to the question,
After 4 years from now,
11x 8/14x 8= 13/16
176x 128 = 182x 104
182x – 176x = 128 – 104
6x = 24=>; x = 24/6 =4
A’s present age = (11x 4) years
= 11 × 4 4 = 48 years

At present, the ratio of the age of Veena and Teena is 6 : 5 and 15 years from now, the ratio will get changed to 9 : 8. Veena’s present age is?

a) 20 years b) 30 years c) 40 years d) 50 years

Ans: b

Solution: Let Veena’s present age be 6x years and Teena’s present age be 5x years.
After 15 years,
6x 15/5x 15 = 9/8
48x 120 = 45x 135
48x – 45x = 135 – 120
3x = 15 Þ x = 5
Veena’s present age = 6x
= 6 × 5 = 30 years

The ratio of ages of two students is 3 : 2. One is older to the other by 5 years. What is the age of the younger student?

a) 10 years b) 2 years c) 5 years d) 5 years

Ans: a

Solution: Let their age be 3x and 2x years.
3x – 2x = 5
x = 5
Younger student’s age
= 2x = 2 × 5 = 10 years

The sum of the age of a father and his son is 100 years now and 5 years ago their age were in the ratio of 2 : 1. The ratio of the age of father and son after 10 years will be?

a) 3 : 5 b) 3 : 1 c) 5 : 3 d) 1 : 3

Ans: c

Solution: 5 years ago, let the age of father = 2x years (let)
Then, Age of son = x years
2x 5 x 5 = 100
3x = 100 –10 = 90
=>; 90/3 = 30
Father’s present age
= 2x 5 = 60 5 = 65 years
Son’s present age = x 5
= 30 5
= 35 years.
After 10 years
Ratio = 65 10/35 10 = 75/45 = 5/3 = 5:3

The ratio of present age of two brothers is 1 : 2 and 5 years back the ratio was 1 : 3. What will be the ratio of their age after 5 years?

a) 2 : 3 b) 3 : 5 c) 4 : 7 d) 5 : 9

Answer: b

Solution: Let the present age of brothers be x and 2x years.
Then, 5 years ago,
x-5/2x-5 = 1/3
3x – 15 = 2x – 5
x = 15 – 5 = 10
Age of elder brother = 10 × 2 = 20
Required ratio = 10 5/20 5 = 15/25 = 3:5

To be continued