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
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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