Question

The average age of $12$ children is $20$ years. If the age of one more child is added, the average is decreased by $1$. What is the age of the child added later ?

• A. $9$ years
• B. $8$ years
• C. $7$ years
• D. $6$ years

Answer 1

The correct option is C $7$ years

Let the age of child added later be $x$ years.

average age of $12$ children $=20\text{years}$

$\therefore$ Total age of $12$ children $=20\times 12=240\text{years}$

After one more child is added-

Average of $13$ children $=20-1=19\text{years}$

Average age of $13$ children $=\frac{\text{sum of 12 children}+x}{13}$

$19=\frac{240+x}{13}$

$\Rightarrow 240+x=247$

$\Rightarrow x=247-240=7\text{years}$

Hence the age of child added later is $7$ years.