Three times the present age of P is 25 years more than the present age of Q. After 10 years, twice the age of Q will be 18 years less than three times the age of P. Find the present age (in years) of Q.

Correct option is C

Given:

Three times the present age of P is 25 years more than the present age of Q.

After 10 years, twice the age of Q will be 18 years less than three times the age of P.

Solution:

Let the present age of P be P years and the present age of Q be Q years.

From the first statement:

3P = Q + 25

Q = 3P – 25……. (1)

After 10 years:

Age of P = P + 10

Age of Q = Q + 10

From the second statement:

2(Q + 10) = 3(P + 10) - 18

2Q + 20 = 3P + 30 - 18

2Q + 20 = 3P + 12

2Q = 3P - 8 ………..(2)

Substitute equation (1) into equation (2):

2(3P - 25) = 3P - 8

6P - 50 = 3P - 8

6P - 3P = -8 + 50

3P = 42

P = 14

Substitute P = 14 into equation (1):

Q = 3(14) - 25 = 42 - 25 = 17 years

Thus, The present age of Q is 17 years.