Madhya Pradesh Police Exam Model Paper 5

Given:
Average age of A, B, C, D = 8 years
Average age of A, B, D, E = 7 years
Age of C = 9 years
Formula used:
Sum of ages = (Average) × (Total number of person)
Calculation:
Sum of ages of A, B, C, D = (Average of A, B, C, D) × 4
$\Rightarrow \mathit{A}+\mathit{B}+\mathit{C}+\mathit{D}=8\times 4=32$ years
$\Rightarrow \mathit{A}+\mathit{B}+9+\mathit{D}=32$
$\Rightarrow \mathit{A}+\mathit{B}+\mathit{D}=23$ ….(1)
Sum of ages of A, B, D, E = (Average of A, B, D, E) × 4
$\Rightarrow \mathit{A}+\mathit{B}+\mathit{D}+\mathit{E}=7\times 4=28$
$\Rightarrow 23+\mathit{E}=28$ [using eqn. 1]
⇒ E = 5 years
∴ The age of sister is 5 years.