Question : The average age of four boys A, B, C, and D is 5 years and the average age of A, B, D, and E is 6 years. C is 8 years old. The age of E is (in years).
Option 1: 12
Option 2: 13
Option 3: 14
Option 4: 15
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Correct Answer: 12
Solution : According to the question, $\frac{A+B+C+D}{4} = 5$ ⇒ $A+B+C+D = 20.$....(i) $\frac{A+B+D+E}{4} = 6$ ⇒ $A+B+D+E = 24$.....(ii) 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) $12 + E = 24$ ⇒ $E = 24 - 12$ ∴ $E = 12$ years Hence, the correct answer is 12.
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