Question

ten years ago, the ratio of two brothers was 1:4. fourteen years from now, the ratio will be 4:7. What is the ratio of their present ages?

Answer 1

The ratio of their age is 3:7.

Explanation:

Given,

10 years ago, the ratio of two brothers was 1:4

After 14 years the ratio will be 4:7

To find the ratio of their present age.

Let,

10 years age their age was x and 4x

So, now their age is (x+10) and (4x+10)

14 years from now their age will be (x+10+14) and (4x+10+14)

That is x+24 and 4x+24

According to the problem,

x+24 : 4x+24 = 4:7

or,
`(x+24)/(4x+24) = (4)/(7)`

or, 7(x+24) = 4(4x+24)

or, 7x+168 = 16x+ 96

or, 16x-7x = 168-96

or, 9x = 72

or, x = 8

Hence,

Their present age is (8+10) and (4×8+10) = 18 and 42

Hence,

The ratio of their age is 18:42 = 3:7