Two numbers are in the ratio of 9 : 11. If 6 added to each number, then the ratio becomes 6 : 7. Find the greater number.

The ratio of two numbers is 9:11.

When 6 is added to each number, the new ratio becomes 6:7.

Let The two numbers be 9x and 11x, where x is the common multiple.

Now, According to the question,

​$$\frac{9x + 6}{11x + 6} = \frac{6}{7}​$$​​

7(9x + 6) = 6(11x + 6)

63x + 42 = 66x + 36

66x - 63x = 42 – 36

3x = 6

x = 2

Now, the two numbers are:

9x = 9 × 2 = 18

11x = 11 × 2 = 22

Thus, the greater number is 22.