Difficult Percentages Solved QuestionAptitude Discussion

Common Information

KK, an aspiring entrepreneur wanted to set up a pen drive manufacturing unit. Since the technology was changing very fast, he wanted to carefully the demand and the likely profits before investing.

The 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 fixed cost to be Rs. 40 lac and variable cost to be Rs. 100 per unit. He expected each pen drive to be sold at Rs. 200

 Q. Common Information Question: 2/2 KK was skeptical that per unit variable cost might increase by $10%$ though the demand might remain same. What will be the expected changes in profit in such a case?
 ✖ A. Profit will increase by $16.67\%$ ✖ B. Profit will increase will by $15.75\%$ ✖ C. Profit would decrease by $15.75\%$ ✔ D. Profit will decrease by $16.67\%$

Solution:
Option(D) is correct

Total cost when 1 lac units were sold when the variable cost has increased by

$10\%=$ Rs. $40$ lac+Rs. $110$ lac = Rs. $150$ lac

Initial Profit at normal variable cost = Rs. 200  lac –  Rs. 140  lac =  Rs. 60  lac

New Profit =  Rs. 200  lac-Rs. 150  lac =  Rs. 50  lac

Therefore percentage decrease in the profit

$=\dfrac{10}{60}\times 100$

$=16.67\%$