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 1,200 and Rs 1,900
• B. Rs 4,200 and Rs 2,800
• C. Rs 5,200 and Rs 2,800
• D. Rs 3,200 and Rs 1,800

Answer 1

The correct option is D 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 $3x=5400=>x=1800$

Substituting $x=1800$ in the equation $\left(1\right)$, we get $4\left(1800\right)+y=10400=>y=3200$

Hence, constant expenses $=Rs3200$ and expenditure per person $=Rs.1800$