Question

Two numbers are in the ratio 4 : 7. If 4 is subtracted from each of the numbers, then the ratio becomes 7 : 13. Find the numbers.

Answer 1

Here, let the two numbers be:

4x and 7x (since they are in the ratio 4 : 7)

According to the given condition:

`(4x - 4)/(7x - 4) = 7/13`

Thus, cross-multiplying the above expression,

13(4x − 4) = 7(7x − 4)

52x − 52 = 49x − 28

52x − 49x = −28 + 52

3x = 24

∴ x = 8

Substituting, x = 8 in 4x and 7x, we get:

4x = 4(8) = 32

7x = 7(8) = 56

Hence, the numbers are 32 and 56.