The average age of four boys A, B, C and D is 5 years and the average age A, B, D, E is 6 years. C is 8 years old. The age of E is (in years) :

Answer: Option A

According to the question,
$$\begin{array}{rl}& \frac{A+B+C+D}{4}=5\\ & A+B+C+D=\mathrm{20.....}(i)\\ & \frac{A+B+D+E}{4}=6\\ & A+B+D+E=\mathrm{24.....}(ii)\end{array}$$
If C = 8 years old, put the value of 'C' in equation (i)
∴ A + B + D + 8 = 20
A + B + D = 12.....(iii)
Put the value of equation (iii) in equation (ii)
12 + E = 24
E = 24 - 12
∴ E = 12