Question

A part of 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 expense is Rs. $ 1000 $ And when it is Rs. $ 240 $ per quintal, the total monthly expenses are Rs. $ 980 $ per quintal. The total quintal. The total monthly expense of the family when the cost of wheat is Rs. $ 350 $ per quintal, will be:
A. \[500\]
B. $ 1200 $
C. $ - 1200 $
D. $ - 500 $

Answer 1

Hint: Let us suppose the constant expenditure is \[x\]and consumption of wheat by the family is $ y $ . According to the first condition. We will change into equation form. After that will use the second condition and make an equation. In these two equations we will find the value of $ x\,\,and\,\,y $ to the answer.

Complete step-by-step answer:
Let the constant expenditure $ = x $
And consumption of wheat by the family $ = y $
Then, according to the information in the question $ x + 250y = 1000 $ …..(I)
And, when the consumption of wheat is ₹ $ 240 $ per quintal and total expenses is ₹ $ 980 $
 $ x + 240y = 980 $ ….(ii)
We will solve equations (i) and (ii) by eliminating method, we have
 $
  \underline
  x + 250y = 1000 \\
   - x + 240y = - 980 \\
    \\
  \,\,\,\,\,\,\,\,10y\,\,\,\,\,\,\,\,\, = \,\,\,\,\,\,20 \\
  $
 $
  10y = 20 \\
  y = \dfrac{{20}}{{10}} \\
  y = 2 \\
  $
Then, the value of y, substitute in the equation for calculating the value of $ x $ , we have
 $
  x + 2 \times 250 = 1000 \\
  x + 500 = 1000 \\
  x = 1000 - 500 \\
  x = 500 \\
  $
Therefore, when the price of wheat is ₹ $ 350 $ per quintal,
Then,
Total expenses $ = x + 350y $ ……(iii)
In the equation, we will substitute the value of $ x\,\,and\,\,y $ , we get
Total expense $ = 500 + 350 \times 2 $
Total expenses $ = 500 + 700 $
Total expenses $ = 1200 $
Thus, total monthly expenses of the family is ₹ $ 1200 $
So, the correct answer is “Option B”.

Note: Students must note that you put the exact value of $ x\,\,and\,\,y $ in the total expenses $ = x + 350y $ to get the answer. And students can also use a substitute method for finding the value of $ x\,\,and\,\,y $ .