Question

The average age of a group of 13 boys is 13.
When two more boys joined the group, the
average rose by 2 years. The sum of the ages
of the two new boys is:​

Answer 1

GIVEN :–

• The average age of a group of 13 boys is 13.

• Two more boys joined the group, the average rose by 2 years.

TO FIND :–

• The sum of the ages of the two new boys = ?

SOLUTION :–

• We know that –

$\\ \implies{ \boxed { \bold{Average = \dfrac{Total \: \: sum \: \: of \: \: ages \: \: of \: \: students}{Total \: \: students}}}}$

• Put the values –

$\\ \implies { \bold{13 = \dfrac{Total \: \: sum \: \: of \: \: ages \: \: of \: \:13\: \: students}{13}}}$

$\\ \implies { \bold{ Total \: \: sum \: \: of \: \: ages \: \: of \: \: 13\:\:students = 13 \times 13}}$

$\\ \implies { \bold{ Total \: \: sum \: \: of \: \: ages \: \: of \: \:13\:\: students = 169\:\:\:\: ----eq.(1)}}$

▪︎When two more boys joined the group, the average rose by 2 years.

▪︎Let the age of two students is 'x' and 'y' , So that –

$\\ \implies { \bold{ \dfrac{Total \: \: sum \: \: of \: \: ages \: \: of \: \:13\:\: students + (x + y)}{13 + 2} = 13 + 2}}$

• Using eq.(1) –

$\\ \implies { \bold{ \dfrac{169+ (x + y)}{13 + 2} = 13 + 2}}$

$\\ \implies { \bold{ \dfrac{169+ (x + y)}{15} = 15}}$

$\\ \implies { \bold{169+ (x + y) = 15 \times 15}}$

$\\ \implies { \bold{169+ (x + y) =225}}$

$\\ \implies { \bold{ x + y=225 - 169}}$

$\\ \implies { \bold{ x + y=56}}$

▪︎ Hence , The sum of the ages of the two new boys is 56 year.

Answer 2

Step-by-step explanation:

${\red{\underline{\underline{\bold{Given:-}}}}}$

• The average age of 13 boys is 13

• When two more boys joined the group, the
• average rose by 2 years

${\blue{\underline{\underline{\bold{To\:Find:-}}}}}$

• The sum of the ages of the two new boys

${\green{\underline{\underline{\bold{Solution:-}}}}}$

The average age of 13 boys is 13

$\boxed{Average=\frac{Sum\:of\:ages\:of\:13\:boys}{Number\:of\:boys}}$

$\implies13 = \frac{Sum \: of \: ages \: of \: 13 \: boys}{13} \\ \\ \implies \: Sum \: of \: ages \: of \: 13 \: boys \: = 169.......(1)$

When two more boys joined the group, the

When two more boys joined the group, theaverage rose by 2 years

Let the ages of two boys be ' x ' and ' y '

$\frac{Sum \: of \: ages \: of \: 13 \: boys + ( x + y)}{13 + 2} = 13 + 2 \\ \\ \implies 169 + (x + y) = 15 \times 15 \\ \\ \implies 169 + (x + y) = 225$

$\implies(x + y) = 225 - 169 \\ \\ \implies x + y = 56$

Therefore,

$\large\purple{\underline{{\boxed{\textbf{Sum\:of\:ages\:two\:new\:boys = 56}}}}}$