Question

114 The average earning of each member of the Ambani family is 20% less than the average earning of each member of the
Sahara family and the total earning of Ambani's family is 20% more than the total earning of Saharas's family. The no of
family members in the Sahara is what percent of the no of family members of Ambani :​

Answer 1

Given :

The average earning of each member of the Ambani family is 20% less than the average earning of each member of the  Sahara family

And

The total earning of Ambani's family is 20% more than the total earning of Sahara's family.

To Find :

The no of family members in the Sahara is what percent of the no of family members of Ambani

Solution :

According to question

Let the number of Ambani family = n

Let the number of Sahara family = m

The average of Ambani family = $\dfrac{a_1+a_2+a_3+...........+_a_n}{n}$

The average of Sahara family = $\dfrac{s_1+s_2+s_3+.......+s_m}{m}$

So, $\dfrac{a_1+a_2+a_3+...........+_a_n}{n}$ = $\dfrac{s_1+s_2+s_3+.......+s_m}{m}$ - 20 % of $\dfrac{s_1+s_2+s_3+.......+s_m}{m}$

i,e  $\dfrac{a_1+a_2+a_3+...........+a_n}{n}$ = 0.8 × $\dfrac{s_1+s_2+s_3+.......+s_m}{m}$       .........1

And

$a_1+a_2+a_3+...........+a_n$ = $s_1+s_2+s_3+.......+s_m$ + 20 % of $s_1+s_2+s_3+.......+s_m$

i.e  $a_1+a_2+a_3+...........+a_n$ =  1.2 × $s_1+s_2+s_3+.......+s_m$           .........2

Solving eq 1 and eq 2

i,e  $\dfrac{1.2 (s_1+s_2+s_3+...........+s_m)}{n}$ = 0.8 × $\dfrac{s_1+s_2+s_3+.......+s_m}{m}$  

Or,   $\dfrac{1.2}{n}$  = $\dfrac{0.8}{m}$

or,    m = $\dfrac{0.8 n}{1.2}$

Or,   m = $\dfrac{2n}{3}$

i.e  m = 0.67 % of n

Hence,  The number of  family members in the Sahara is 0.67 % of the number of family members of Ambani   Answer