Question

the two numbers are in the ration 2:3. on adding 8 to each of the numbers, we obtain numbers in the ratio 5:7. find the original numbers.

Answer 1

Let the common ratio be 'x'.

Given that the numbers are in the ratio of 2:3.

Hence, the numbers are 2x and 3x.

(i)

Given that on adding 8 to each of the numbers, we obtain in the ratio 5:7.

⇒ (2x + 8) : (3x + 8) = 5 : 7.

⇒ 7(2x + 8) = 5(3x + 8)

⇒ 14x + 56 = 15x + 40

⇒ -x = -16

⇒ x = 16.

Then:

⇒ 2x = 32

⇒ 3x = 48.

Therefore, the numbers are 32 and 48.

Hope this helps!

Answer 2

Please see the attachment