Question:hard

KK, an aspiring entrepreneur, wanted to set up a pen drive manufacturing unit. Since technology was changing very fast, he wanted to carefully judge the demand and the likely profit before investing. A market survey showed he could sell 1 lac (100000) units before customers moved to other gadgets. KK had to bear two kinds of cost: fixed cost (the cost that does not change no matter how many units are made) and variable cost (variable cost per unit times the number of units). He expected the fixed cost to be Rs. 40 lac and the variable cost to be Rs. 100 per unit. He expected to sell each pen drive at Rs. 200.

He discussed his business with a chartered accountant. KK said he was thinking of a loan of Rs. 20 lac at simple interest of \(10\%\) per year to start the business. The chartered accountant told him that in this case KK has to pay interest, followed by \(30\%\) tax. By how much does KK's earnings change with a \(20\%\) growth in sales as against the original sales volume, in both cases considering tax and interest on the loan?

Show Hint

Work out net profit (after loan interest and 30% tax) at the original 1 lac units, then again at 1.2 lac units, and compare the two.
Updated On: Jul 10, 2026
  • 20%
  • 16.7%
  • 25.6%
  • 34.5%
Show Solution

The Correct Option is D

Solution and Explanation

Step 1: Understanding the Approach:
Instead of recalculating the whole profit and loss twice, we can track just the change caused by the extra sales, since the fixed cost and the loan interest never move.

Step 2: Key Formula:
Each extra unit sold adds its full selling price minus its variable cost to profit before interest and tax (EBIT), because fixed cost is already covered by the original volume. So the rise in EBIT equals the rise in contribution, and fixed cost cancels out of the change.

Step 3: Detailed Working:
Contribution per unit $= 200 - 100 = Rs. 100$.
At the original volume of $100000$ units, contribution $= 100000 \times 100 = Rs. 1,00,00,000$, and EBIT $= 1,00,00,000 - 40,00,000 = Rs. 60,00,000$.
A $20\%$ jump in sales adds $20000$ extra units, worth $20000 \times 100 = Rs. 20,00,000$ of extra contribution. Since fixed cost stays put, EBIT simply rises by this same Rs. $20,00,000$, from Rs. $60,00,000$ to Rs. $80,00,000$.
The loan interest of Rs. $2,00,000$ a year is fixed too, so profit before tax rises from $60,00,000 - 2,00,000 = Rs. 58,00,000$ to $80,00,000 - 2,00,000 = Rs. 78,00,000$, a rise of exactly Rs. $20,00,000$, since the fixed interest cancels out of the difference.
Tax is charged at a flat $30\%$ on profit before tax in both years, so the $(1-0.30)$ factor sits on both the original and the new figure and cancels out when we take a percentage change. This means the percentage change in profit after tax is the same as the percentage change in profit before tax.

Step 4: Final Answer:
Percent change $= \dfrac{20,00,000}{58,00,000} \times 100 \approx 34.5\%$.
So KK's earnings rise by about $34.5\%$, matching option E.
Was this answer helpful?
0

Top Questions on Profit and Loss

Questions Asked in XAT exam

Read the scenario and answer the question:
The upper hinge of a dataset is the median of all the values to the right of the median of the dataset in an ascending arrangement, while the lower hinge of the dataset is the median of all the values to the left of the median of the dataset in the same arrangement.
For example, consider the dataset 4, 3, 2, 6, 4, 2, 7. When arranged in the ascending order, it becomes 2, 2, 3, 4, 4, 6, 7. The median is 4 (the bold value), and hence the upper hinge is the median of 4, 6, 7, i.e., 6. Similarly, the lower hinge is 2. 
A student has surveyed thirteen of her teachers, and recorded their work experience (in integer years). Two of the values recorded by the student got smudged, and she cannot recall those values. All she remembers is that those two values were unequal, so let us write them as A and B, where A < B. The remaining eleven values, as recorded, are: 5, 6, 7, 8, 12, 16, 19, 21, 21, 27, 29. Moreover, the student also remembers the following summary measures, calculated based on all the thirteen values: 
Minimum: 2
Lower Hinge: 6.5 
Median: 12 
Upper Hinge: 21 
Maximum: 29
View Solution
Read the following scenario and answer the questions that follow.
A T20 cricket match consists of two teams playing twenty overs each, numbered 1 to 20. The runs scored in any over is a non-negative integer. The run rate at the end of any over is the average runs scored up to and including that over, i.e., the run rate at the end of the kth over is the average number of runs scored in overs numbered \(1, 2, …, k,\) where \(1 \leq k \leq 20, k\) a positive integer.
The following table indicates the run rate of a team at the end of some of the overs during a T20 cricket match (correct up to 2 decimal places), where \(1 \leq N – 2 < N + 6 \leq 20\), N a positive integer. It is also known that the team did not score less than 6 runs and more than 15 runs in any over.
Over NumberRun Rate
N-28.00
N7.43
N+28.11
N+48.45
N+68.08
View Solution