Two numbers are in the ratio of 15:11. If their H.C.F. is 13, find the numbers.

To find the two numbers when their ratio and Highest Common Factor (H.C.F.) are known, you can use a direct multiplication approach.

The Concept
When two numbers are given in a ratio a:b, they can be represented as a * x and b * x, where x is the common factor. In this case, the H.C.F. of the numbers is precisely that common factor, x.

Calculation
Given Ratio: 15:11

Given H.C.F.: 13

Identify the Numbers:

First number = 15 * 13 = 195

Second number = 11 * 13 = 143

The numbers are 195 and 143.