Question

The average age of a group of 12 students is 20 years. If 4 more students join the group, the average age
increases by 1 year. The average age of the new students is:​

Answer 1

Given :

• average age of first 12 students = 20 year

• average age after the joining of 4 new students = (average age of first 12 students + 1 year ) = 20 + 1 = 21 years

To Find : average age of 4 new students

• { average age of 4 new students = sum of ages of 4 new students ÷ 4 }

Let :

• sum of ages of first 12 students = x
• sum of ages of 4 new students = y

Formula used :

$average \: age = \dfrac{sum \: of \: age \: of \: all \: students}{number \: of \: sudents}$

Solution :

$average \: age \: of \: first \: 12 \: students = \dfrac{ sum \: of \: age \: of \: first \: 12 \: students }{12}$

putting values, we get ;

$20 \: = \: \dfrac{x}{12} \\ \\ x \: = 20 \times 12 \\ \\ x = \: 240 \: years$

also ,

average age after the joining of 4 new students = $\dfrac{sum \: of \: ages \: of \: first \: 12\: students \: + \: sum \: of \: ages\:of \:4 \: new \: students}{12 + 4}$

putting value, we get ;

$21 \: = \: \dfrac{(x + y)}{16} \\ \\ (x + y) \: = \: 21 \times 16 \\ \\ (x + y) \: = \: 336 \\ \\ y \: = \: 336 \: - \: x$

putting value of x in above equation , we get ;

y = 336 - 240

y = 96 years

therefore,

$average \: age \: of \: 4 \: new \: students \: = \: \dfrac{sum \: of \: ages \: of \: 4 \: new \: students \: }{4} \\ \\ \\ average \: age \: of \: 4 \: new \: students \: = \: \dfrac{y}{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

putting value of y in above equation, we get ;

$average \: age \: of \: 4 \: new \: students \: = \: \dfrac{96}{4} \\ \\ average \: age \: of \: 4 \: new \: students \: = \: 24$

ANSWER : 24 years