Question

4 years ago, the ratio of the ages of A and B was 2 : 3 and after 4 years it becomes 5:7. Find their
present ages.​

Answer 1

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let the ages be ...

4-(2x+3x)=4+(5x+7x)

4-5x=4+11x

-5x=4+4+11x

-5x-11x=8

16x=8

x=8/16

x=2

2x=2(2)=4

3x=3(2)=6

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Answer 2

Let A’s age be 2x and B’s 3x

Since this was their age 4 years ago, four years hence their ages = 4+4= 8 years

2x:3x = 2x/3x

2x+8/3x+8 = 5/7

By cross multiplication,

7(2x+8) = 5(3x+8)
14x + 56 = 15x + 40
- 40 + 56 = 15x - 14x
x = 56 - 40

Thus,

x = 16

A’s age 4 years ago = 2*16=32
B’s age 4 years ago = 3*16=48

32+4 = 36 is A’s present age
48+4 = 52 is B’s present age



Hope it helps ..