Question

10. The average age of 10 members in a family is 21 years
and due to death of one family member, the average age is
reduced by 2 months. The age of the member who died is
(a) 20 years 10 months (5) 20
years
3
(c) 225 years
(d) 19
years
​

Answer 1

Answer :

The age of the member who died is 22.5 years.

Step-by-step explanation :

Given :

• The average age of 10 members in a family is 21 years
• Due to death of one family member, the average age is  reduced by 2 months.

To find :

The age of the member who died

Solution :

  $\boxed{\tt Average=\dfrac{Sum \ of \ observations}{Number \ of \ observations}}$

The average age of 10 members = 21 years

  $\sf 21 \ years=\dfrac{Sum \ of \ 10 \ members' \ age}{10} \\\\ 21 \times 12 \ months=\dfrac{Sum \ of \ 10 \ members' \ age}{10} \\\\ \sf Sum \ of \ 10 \ members' \ age=252 \times 10 \ months \\\\ \sf Sum \ of \ 10 \ members' \ age=2520 \ months$

One of the member of the family died. Let the age of this person be x years.

  ➙  Sum of 10 members' age = Sum of 9 members' age + Age of the person died

 ➙ 2520 months = Sum of 9 members' age + x years

 ➙ 2520 months = Sum of 9 members' age + 12x months

 ➙ Sum of 9 members' age = (2520 - 12x) months

The average is reduced by 2 months.

➙ New average = 21 years - 2 months

➙ New average = (21×12) months - 2 months

➙ New average = 252 - 2 months

➙ New average = 250 months

   $\sf New \ average=\dfrac{Sum \ of \ 9 \ members' \ age}{9} \\\\ \sf 250 \ months =\dfrac{(2520-12x) months}{9} \\\\ \sf 2520-12x=250 \times 9 \\\\ \sf 2520-x=2250 \\\\ x=2520-2250 \\\\ \sf x=270 \ months$

Now, we have to convert 270 months to years.

  Divide by 12,

$\sf = \dfrac{270}{12} \\\\ \sf =\dfrac{6 \times 45}{6 \times 2} \\\\ \sf =\dfrac{45}{2} \\\\ \sf =22.5 \ years$

= 22 years 6 months

Therefore, the age of the person who died is 22.5 years