Question

The ratio of two numbers is $\frac{2}{3}$. If 2 is subtracted from the first and 8 from the second, the ratio becomes the reciprocal of the original ratio. Find the numbers.

Answer 1

Let the two numbers be x and y

According to the question,

3x - 2y = 0 ...(1)

Also,

2x - 3y = -20 ...(2)

Multiplying equation no. (1) by 2 and (2) by 3 and substracting

From (1), we get

3x - 2(12) = 0

x = 8

Thus, the numbers are 8 and 12.