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Five years ago, the average of P and Q was 15 years. Average P, Q and R is 20 years. How old will R be after 10 years?

Five years ago, the average of P and Q was 15 years. Average P, Q and R is 20 years. How old will R be after 10 years?

  • (A) 35 years
  • (B) 40 years
  • (C) 30 years
  • (D) 50 years
  • Solution: Assume that the current ages are P, Q, and R.
  • Step 1 - using the first condition:
  • Five years ago, the average of P and Q was 15.
  • So, we can write:
  • [(P - 5) + (Q - 5)]/2 = 15, which can be simplified to:
  • (P + Q - 10)/2 = 15, and then P + Q - 10 = 30, so P + Q = 40.
  • Step 2 - using the second condition:
  • The average of P, Q, and R is 20, so:
  • (P + Q + R)/3 = 20, giving P + Q + R = 60, and then P + Q + 20 = 60, since we found P + Q = 40, so 40 + 20 = 60, giving R = 20.
  • Step 3 - find the age of R in 10 years:
  • R + 10 = 20 + 10 = 30.
  • Thus, the correct answer is option (C) 30 years.
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March 18, 2026 No Comments
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