Question

A part of the monthly expenses of a family is constant and the remaining varies with the price of wheat. When the price of wheat is Rs. $250$ per quintal, the total monthly expenses are Rs. $1000$ and when it is Rs. $240$ per quintal, the total monthly expenses are Rs. $980$ per quintal. The total monthly expenses of the family when the cost of wheat is Rs. $350$ per quintal, will be:

• A. Rs. $500$
• B. Rs. $1200$
• C. Rs. $-1200$
• D. Rs. $-500$

Answer 1

The correct option is B Rs. $1200$

Let the constant part of the expenditure $=$ Rs. $x$
and the variable part $=$ Rs. $y\times$ price of wheat.
Given that when the price of wheat is Rs. $250$ per quintal, the total expenses are Rs. $1000$.
$\therefore x+250y=1000...\left(1\right)$
Given also that when the price of wheat is Rs. $240$ per quintal, the total expense are Rs. $980$
$\therefore x+240y=980...\left(2\right)$
Subtracting $\left(2\right)$ from $\left(1\right)$,
$10y=20⟶y=2$
Substituting this value of $y$ in $\left(1\right)$
$x+250\left(2\right)=1000$
$\Rightarrow x=1000-500=500$
Therefore, when the price of wheat is Rs. $350$ per quintal,
Total expenses $=x+350y=500+350\left(2\right)=$ Rs. $1200$
$\therefore$ total expenses $=$ Rs. $1200$