Question
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
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