Question

The mean age of 6 boys in a class is 12. Three new boys are admitted to the class. If the mean age of the class is now 13, what is the sum of the ages of the three new boys?

Answer 1

${\underline{\underline{\red{\sf{Given:}}}}}$

• Mean ages of 6 boys in a class is 12.
• Three new boys are added to class.
• The new mean age becomes 13.

${\underline{\underline{\red{\sf{To\:Find:}}}}}$

• The sum of ages of the new boys.

${\underline{\underline{\red{\sf{Answer:}}}}}$

Let us take the sum of ages of three boys be x .

Now ,we know the formula of mean as ;

$\large{\underline{\boxed{\red{\sf{\leadsto Mean=\dfrac{Sum\:of\:all\:terms}{Number\:of\:terms}}}}}}$

Again let sum of ages of initial 6 boys be y.

Atq, $\sf{Mean=\dfrac{Sum\:of\:terms}{Number\:of\:terms}}$

$\sf{\implies 12=\dfrac{y}{6}}$

$\sf{\implies y=12\times6}$

$\sf{\mapsto y=72}$

$\rule{200}1$

Again given that new mean is 13 .So ,

Atq,$\sf{\implies 13=\dfrac{Sum\:of\:age\:of\:3\:boys+Sum\:of\:Age\:of\:6\: initial\:boys}{Total\: number\:of\:boys}}$

$\sf{\implies 13=\dfrac{x+72}{6+3}}$

$\sf{\implies 13=\dfrac{x+72}{9}}$

$\sf{\implies (x+72)=13\times 9}$

$\sf{\implies x+72=117}$

$\sf{\implies x=117-72}$

${\underline{\boxed{\purple{\sf{\leadsto x=45}}}}}$

$\sf{\orange{Hence\:sum\:of\:ages\:of\:3\:new\:boys\:is\:45\:years}}$