If 2 is added to each of two given numbers, their ratio becomes 1 : 2. However, if 4 is subtracted from each of the given numbers, the ratio becomes 5 : 11. Find the numbers.

Question

Philoid · Accepted Answer

Let the two numbers be x and y.

According to question -

On Cross multiplying, we get -

⇒ 2x + 4 = y + 2

⇒ 2x - y = - 2.....(1)

and,

⇒ 11x - 44 = 5y - 20

⇒ 11x - 5y = 24

From equation (1), we get -

x = (y - 2)/2

Substituting the value of x in equation (2), we get -

⇒ y - 22 = 48

∴ y = 70

substituting the value of y in equation (3), we get -

x = 34

Thus, the numbers are 34 and 70.