The ratio of x and y is 9 : 16. If both x and y are increased by 15, then the ratio becomes 2:3. Find x and y.

A 27 and 48

B 36 and 48

C 18 and 32

D 24 and 36

E 18 and 24

Correct Answer: Option A

Let both the numbers be x and y

Therefore, x/y = 9/16 ⇒ x = 9y/16……(1)

And, (x+15)/(y+15) = 2/3 → 3x - 2y = -15…..(2)

Substituting the value of x in (2).

3(9y/16) - 2y = -15

⇒ 27y/16 - 2y = -15

⇒ y = 48

Putting the value of y in 1

We get, x = (9 x48)/16

⇒ x = 27