Question

The sum of the present ages of P and Q is 120 years. Also 15 years ago, the ratio of the ages of P and Q was 6/3 . Find the present age of P.​

Answer 1

Step-by-step explanation:

let the present age of P be x and Q be y.

Given :-

P + Q = 120

x+y = 120. (i)

15 years ago

age of P = x-15

age of Q = y-15

ratio = x-15/y-15 = 6/3

3(x-15) = 6(y-15)

3x-45 = 6y-90

3x-6y = -45 (ii)

multiplying equation (i) by 3

(x+y = 120)×3

3x+3y = 360. (iii)

eliminating equation (ii) and (iii), we get

3x-6y = -45

3x+3y = 360

- - -

_____________

-9y = -405

y = 49

putting the value of y in equation (i),we get

x+y = 120

x+49 = 120

x = 71

hence, the present age of P = X = 71 years

and the present age of Q = y = 49 years.