Question

Average age of n men ina group is 33 years.if 5 new men whose average age is 41 year join the group then the average of group Becomes 35 years.find the value of n?

Answer 1

Answer:

The value of n for the given average expression is 15 .

Step-by-step explanation:

Given as :

The average of n men in a group = 33 years

i.e $\dfrac{a_1 + a_2 + a_3 ......+ a_n}{n}$ = 33

Or, $a_1 + a_2 + a_3 + ..... +a_n$ = 33 n           .........A

Again

The average of 5 men = 41 years

I.e $\dfrac{b_1 + b_2 + b_3 + b_4 + b_5}{5}$  = 41

Or, $b_1 + b_2 + b_3 + b_4 + b_5$ = 41 × 5

Or,  $b_1 + b_2 + b_3 + b_4 + b_5$ = 205            ........B

Again

The average of 5 + n men = 35 yearsn

i.e $\dfrac{a_1 + a_2 + a_3 + ....... + a_n + b_1 + b_2 + b_3 + b_4 + b_5}{n + 5}$ = 35

Or, $a_1 + a_2 + a_3 + ...... + a_n + b_1 + b_2 + b_3 + b_4 + b_5$ = 35 × ( n + 5 )

Or, 33 n + 205 = 35 n + 35 × 5

Or, 205 - 175 = 35 n - 33 n

Or, 2 n = 30

∴   n = $\dfrac{30}{2}$

i.e  n = 15

So, The value of n for the given average expression = n = 15

Hence, The value of n for the given average expression is 15 . Answer