Question

The ratio of present ages of X and Y is 4:5. Which of the following can't be the ratio of ages of X and Y, 20 years ago ?
A) 2 : 5
B) 8 : 15
C) 9 : 10
D) 3 : 5

Answer 1

The ratio of the present ages of A:B::4:7, or

7A = 4B, or

A = (4/7)B …(1).

Ten years hence the ratio of their ages will be (A+10):(B+10)::3:4, or

4(A+10) = 3(B+10), or

4A = 3B+30–40 = 3B-10, or

A = (3/4)B -2.5 …(2)

Equate (1) and (2)

A = (4/7)B = (3/4)B -2.5. LCM of 7 and 4 is 28, So we have

16B = 21B -2.5*28 = 21B- 70, or

21B - 16B = 70, or

5B = 70, or

B = 14. From (1), A = (4/7)*14 = 8.

So the ratio of A’s age 5 years later to the present age of B will be 13:14.

Answer 2

Let me introduce the reader to a simple method to attempt such questions.

Current ratio = 5:4

= 10:8 ( both ratios are equivalent)

Required ratio after 3 years = 11:9

We observe the difference between numerator and denominator is same, 2 , in both cases.Comparing numerator with numerator and denominator with denominator, we find the gap is same ( 11 - 10 = 1) & (9 - 8 = 1)