Question

The manufacturer of a certain item can sell all he can produce at the selling price of Rs 60 each. It costs him Rs 40 in materials and labour to produce each item and he has overhead expenses of Rs 3000 per week in order to operate the plant. The number of units he should produce and sell in order to make a profit of at least Rs 1000 per week, is:
A. 200
B. 250
C. 300
D. 400

Answer 1

- Hint: We will be using the concept of profit and loss to solve the problem. We will be using the concept of word problem to make equations as per the data given in the question and then we will simplify the equation for the value of the number of units he should produce and sell to make profit.

Complete step-by-step solution -

We have been given the selling price of an item is Rs 60. It has also been given that the materials and labour cost to produce each item is Rs 40.
Also, the overhead expenses of a week = Rs. 3000
Now, we have to find the number of units he should produce and sell to earn a profit of at least Rs 1000 per week.
Let us take the number of items produced in a week = x
Therefore, the total cost of x items = 40x + 3000
Now, total selling price of x items = 60x
Now, it has been given that the profit should be less at least Rs 1000 per week.
Therefore,
$\begin{align}
  & \text{selling price }-\ \text{cost price}>1000 \\
 & 60x-40x-3000\ge 1000 \\
 & 20x\ge 4000 \\
 & x\ge 200 \\
\end{align}$
Therefore, the number of units is 200.
Hence, the answer is option (A).

Note: To solve these types of questions it is important to convert the condition given in question to equation and then solve. Also it has to be noted that overhead expenses are per week not per item and we have not included them per item instead add them in total expense per week.