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### Question

The average age of three friends 3 years ago was 31 years. The average age of two them 5 years ago was 12 years. What is the present age of the third friend?

**A**

68 years.

**B**

69 years.

**C**

67 years.

**D**

66 years.

**Soln.**

**Ans: a**

Let the present ages of the three friends be a, b and c. We are given ${(b - 5) + (c - 5)}/2$ = 12. Which gives b + c = 34. We are also given ${(a - 3) + (b - 3) + (c - 3)}/3$ = 31, which gives a + b + c = 3 * 31 + 9 = 102. Putting b + c here we get a = 102 - (b + c) = 102 - 34 = 68 years.