In 5 years from now, the ratio of ages of P and Q will be 9:5. If age of P after 15 years is 150% more than age of Q 12 years ago, find the difference between their current ages.

Solution

Let present ages be P = p, Q = q

(p + 5)/(q + 5) = 9/5

=> 5(p + 5) = 9(q + 5)

=> 5p + 25 = 9q + 45

=> 5p = 9q + 20 ...(1)

150% more means 2.5 times

P after 15 years = 2.5 × (Q 12 years ago)

=> p + 15 = 2.5(q - 12)

=> p + 15 = 2.5q - 30

=> p = 2.5q - 45

Multiply by 2: 2p = 5q - 90 ...(2)

Now use (1):

5p = 9q + 20

Multiply by 2: 10p = 18q + 40 ...(3)

From (2): 2p = 5q - 90

Multiply by 5: 10p = 25q - 450 ...(4)

Equate (3) and (4):

18q + 40 = 25q - 450

490 = 7q

q = 70

Put q = 70 in (1):

5p = 9(70) + 20 = 650

p = 130

Difference = p - q = 130 - 70 = 60