Two numbers are in the ratio 5:6., find the numbers.


Question: Two numbers are in the ratio 5 : 6. If 8 is subtracted from each of the numbers, the ratio becomes 4 : 5, find the numbers.

The question is based on the concepts of linear equations in two variables and ratios.

Answer:  The two numbers are 40 and 48, which are in the ratio 5 : 6.

Let's find the numbers.

Explanation:

Let the numbers be 5x and 6x.

Given that, if 8 is subtracted from each of the numbers, the ratio becomes 4:5.

(5x - 8) : (6x - 8) = 4 : 5

(5x - 8) / (6x - 8) = 4 / 5

5(5x - 8) = 4(6x - 8)

25x - 40 = 24x - 32

25x - 24x = 40 - 32

x = 8

the first number = 5x = 5 × (8) = 40

the second number = 6x = 6 × (8) = 48

Thus, the numbers are 40 and 48 which are in the ratio 5 : 6.