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The ages of P, Q and R form an arithmetic progression. After 5 years, the ratio of ages of Q and R will be 6 : 7. Difference between ages o…

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The ages of P, Q and R form an arithmetic progression. After 5 years, the ratio of ages of Q and R will be 6 : 7. Difference between ages of P and Q is 6 years. What was P’s age 3 years back?
  • A20 years
  • B21 years
  • C22 years
  • D24 years
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The ages of P, Q and R form an arithmetic progression. Difference between ages of P and Q is 6 years. So, difference between ages of Q and R would also be 6 years.

Let age of Q be T years, and that of R be (T + 6) years.

After 5 years, the ratio of ages of Q and R will be 6 : 7.

⇒ (T + 5)/(T + 11) = 6/7

⇒ 7T + 35 = 6T + 66

⇒ T = 31

Age of Q = 31 years

⇒ Age of P = 6 years lesser than age of Q = 25 years

∴ 3 years back, age of P was 22 years.