In a company, the cost of producing one item is Rs. 100, if the item is sold at Rs. 150 and Rs. 50,000 is the fixed cost of the company, then the break-even point is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 1000 items
At the break-even point, revenue equals total cost. For x items:
\( \displaystyle R(x)=150x \)
\( \displaystyle C(x)=50000+100x \)
\( \displaystyle 150x=50000+100x \)
\( \displaystyle 50x=50000 \)
\( \displaystyle x=1000 \)
The break-even point is 1000 items.
Shortcut: Each item contributes 150 − 100 = Rs. 50 towards the fixed cost, so the fixed cost is covered after \( \frac{50000}{50}=1000 \) items.
NCERT (2026-27 edition):
Mathematical Modelling
