Two numbers are in the ratio of 7 : 8. If the difference between the numbers…

Concept

When two numbers are in the ratio a : b, they can be represented as ax and bx, where x is a common scale factor.

Their difference is (b − a)x, so the given difference determines the scale factor.

Application

1. Represent the two numbers as 7x and 8x.

2. Use the difference: 8x − 7x = x = 30, so x = 30.

3. Substitute x = 30: 7x = 210 and 8x = 240.

Cross-check

The difference is 240 − 210 = 30, and 210 : 240 reduces to 7 : 8 after division by 30.

Result

Therefore, the numbers are 210 and 240.