Question

If the ages of A and C are added to twice the age of B, the total becomes 73. If the ages of B and C are added to thrice the age of A, the total becomes 84 and if the age of A is added to thrice the age of B and thrice and age of C, the total becomes 124. What is the age of A?

• A.
  16 years
• B.
  15 years
• C.
  12 years
• D.
  21 years
• E. None of the above

Answer 1

The correct option is C

12 years
A + C + 2B = 73 ...... (1)
B + C + 3A = 84 .... ...(2)
A + 3B + 3C = 124 .......(3)
Multiply equation 2 by 3 and subtract 3
(3B + 3C + 9A = 252) - (A + 3B + 3C = 124) $\Rightarrow$ 8 A = 128
$\Rightarrow$ A = 12 Years