Question

KK, an aspiring entrepreneur wanted to set up a pen drive manufacturing unit. Since technology was changing very fast, he wanted to carefully gauge the demand and the likely profits before investing. Market survey indicated that he would be able to sell 1 lac units before customers shifted to different gadgets. KK realized that he had to incur two kinds of costs: fixed costs (the costs which do not change, irrespective of the number of units of pen drives produced) and variable costs (= variable cost per unit multiplied by the number of units). KK expected the fixed cost to be Rs. 40 lac and the variable cost to be Rs. 100 per unit. He expected each pen drive to be sold at Rs. 200.

KK was skeptical that the variable cost per unit might increase by 10 percent, though the demand might remain the same. What will be the expected change in profit in such a case?

• A. Profit would decrease by 10.33%
• B. Profit will increase by 15.75%
• C. Profit would decrease by 15.75%
• D. Profit will decrease by 16.67%

Hint:

Only the variable cost changes here; find the extra total variable cost from the 10 percent hike and compare it to the original profit to get the percentage fall.

Answer 1

The Correct Option is D

Instead of recomputing the full profit figure, this approach tracks only the extra cost the 10 percent hike adds, and compares that directly to the original profit.

1. Find the extra variable cost caused by the hike: the variable cost per unit rises by 10% of Rs. 100, which is Rs. 10 per unit. Over 1,00,000 units (demand stays the same), the extra cost is $10 \times 1,00,000 = 10,00,000$ rupees.
2. Note that revenue and fixed cost do not change: demand is unchanged, so revenue stays at $1,00,000 \times 200 = 2,00,00,000$, and fixed cost stays at Rs. 40 lac. Only the variable cost line goes up.
3. Since profit = revenue minus total cost, and only cost increases, profit falls by exactly the extra cost: new profit = old profit minus Rs. 10,00,000.
4. Find the original profit to use as the base for the percentage: original total cost = $40,00,000 + (100)(1,00,000) = 1,40,00,000$, so original profit = $2,00,00,000 - 1,40,00,000 = 60,00,000$.
5. Compute the percentage fall: $\dfrac{10,00,000}{60,00,000} \times 100 = 16.67\%$.

So profit falls by 16.67%, which is option D. Options built around 10.33% or 15.75% come from comparing the extra cost to the wrong base, such as revenue instead of the original profit.

Let's summarize:

• When only variable cost changes and demand stays fixed, the drop in profit exactly equals the extra total variable cost.
• The percentage change must always be measured against the original profit, not against revenue or total cost.

So profit will decrease by 16.67%.