Question

A part of monthly expenses of a family is constant and the remaining vary with the number of members in the family. For a family of $4$ person, the total monthly expenses are Rs. $10,400$ whereas for a family of $7$ persons, the total monthly expenses are Rs. $15,800$. Find the constant expenses per month and the monthly expenses of each member of a family.

• A. Rs. $3,220$ and Rs. $1,800$
• B. Rs. $3,100$ and Rs. $1,800$
• C. Rs. $3,200$ and Rs. $1,800$
• D. Rs. $3,300$ and Rs. $1,800$

Answer 1

The correct option is C Rs. $3,200$ and Rs. $1,800$

Let the number of family members be $x$ and the constant expense be $y$.
Given, $4x+y=10400$ ....(1)
And $7x+y=15800$ ....(2)
Subtracting equation $\left(1\right)$from $\left(2\right)$, we get

$3x=5400$

$\Rightarrow x=1800$
Substituting $x=1800$ in the equation $\left(1\right)$, we get

$4\left(1800\right)+y=10400$

$\Rightarrow y=3200$

Hence, constant expenses $=$ Rs. $3200$ and expenditure per person $=$ Rs. $1800$.