Question

The average age of three friends A, B, and C is 7 years. Five years later, the average age of A and C will be 1½ years more than B's age then. How old will B be 10 years hence (in years)?

Options

• 6 years

• 8 years

• 12 years

• 16 years

Answer 1

Suppose the present ages of the three friends are A, B and C respectively.
We know that A + B + C = 21.
Five years later, their ages would be (A + 5), (B + 5) and (C + 5) respectively.
So, (A + 5 + C + 5) / 2 = (B + 5) + 3/2, which on simplifying gives A + C + 10 = 2B + 13. From the first expression we know that A + C = 21 – B.
Substituting this value in the second expression,
we get 21 – B +10 = 2B + 13 or 3B = 18,
which yields B = 6 years.
Thus, 10 years hence, B will be 16 years old.
So, option 16 years is the correct answer.