Question

Average age of 5 boys is 13 yr. One more boy
joins them and the average nge becomes 12
yr. The age of the boy who joins les
(A) 12 yr (B) 13 y
(C) 14 ye (D) 7y​

Answer 1

Answer:

Let the sum of of Ages of 5 boys be = y

ACCORDING TO THE QUESTION

avg.of their ages is 13yrs.

i.e.

$avg. = \dfrac{sum \: of \: their \: ages}{no \: of \: boys} \\ \\ 13 = \frac{y}{5} \\ \\ y = 13 \times 5 \\ \\ \blue{\Large \boxed{{\boxed{y= 65yrs}}}}$

Now

Let

age of 6th boy be = x

Now New avg. becomes 12yrs

i.e.

$\dfrac{y + x}{6} = 12 \\ \\ y + x = 72 \\ \\ 65 + x = 72 \\ \\ x =72 - 65 \\ \\ \blue{\Large{ \boxed {\boxed{\boxed{\boxed{x = 7yrs}}}}}}$

So age of 6th boy is 7yrs .

Hence option D is correct.