The ratio of age of P and Q is 10 : 13. The ratio of age of P, ten years ago to the age of Q after ten years is 8 : 15. Find ratio of age of P, ten years hence to the age of Q ten years ago.
Answer & explanation
Correct answer: option 3
ratio of → P : Q
10 : 13
Let Present age of P = 10x and Present age of Q = 13x
According to question , Ratio of age of P 10 years ago to the age of Q after 10 year is 8 : 15 .
i.e. ratio of → P : Q
8 : 15
i.e. \(\frac{10x\;-\;10}{13x\;+\;10}\) = \(\frac{8}{15}\)
150x - 150 = 104x + 80
46x = 230
x = 5
As, Present age of P = 10x
P's present age = 10 × 5 = 50
Q's present age = 13 × 5 = 65
Ratio of age of P 10 year hence= 50 + 10 =60
Ratio of age of Q 10 years ago = 65 - 10 =55
required ratio, P : Q
60 : 55
12 : 11