Question

15. In a village the average age of n people is 39 years. But after the verification it was found that one person was 40 year older than his age considered in the average. So the new average, after correction increased by 1. The value of n is?​

Answer 1

Given :- In a village the average age of n people is 39 years. But after the verification it was found that one person was 40 year older than his age considered in the average. So the new average, after correction increased by 1. The value of n is ?

Solution :-

→ Average of n people = 39 years.

so,

→ Total ages of all people= 39 * n = 39n years.

now, given that, one person was 40 year older than his age considered in the average.

so,

→ sum of all people now = (39n + 40) years.

then,

→ New Average = 39 + 1

→ (Total age) / Total people = 40

→ (39n + 40) / n = 40

→ 39n + 40 = 40n

→ 40n - 39n = 40

→ n = 40 (Ans.)

Hence, value of n is 40.

Answer 2

Given:

• In a village the average age of n people is 39 years.
• After the verification it was found that one person was 40 year older than his age considered in the average.
• The new average, after correction increased by 1.

Solution:

To find the value of n = ?

Average of n people = 39 years.

Total ages of all people = 39 × n = 39n years.

Now,

Sum of all people = (39n + 40) years.

=> New average = 39 + 1

=> Total age/Total people = 40

=> (39n + 40)/n = 40

=> 39n + 40 = 40

=> 40n - 39n = 40

=> n = 40

$\qquad \large \dag{\underline{\boxed{\bf n = 40}}}$