Question

The mean income of I group of persons is Rs. $400$ II group of persons has mean income Rs. $480$. If the mean income of all $160$ persons in the two groups together is Rs. $430$, then the number of person in the II group is

• A. $100$
• B. $50$
• C. $60$
• D. None of these

Answer 1

The correct option is C $60$

The mean income of group of person is Rs. $400$

II group$=480$, if the mean income of all $160$ person in the two groups is Rs. $430$, then the no of person group II is?

Solution:

Let the number of people in $1^{st}$ group$=$x

Let the number of people in $2$nd group$=$y

given $x+y=160$ .......$\left(1\right)$

Total income from $1^{st}$ group$=400x$

Total income from $2$nd group$=480y$

Mean income of both group$=430$

i.e

$\frac{400x+480y}{x+y}=430$

$400x+480y=430x+430y$

$30x+8.50y=0$

Solving equation I and II

$y=60$

No. of people in $2^{nd}$ group$=60$.