Question 3

A Techno company has 14 machines of equal efficiency in its factory. The annual manufacturing costs are Rs. 42,000 and establishment charges are Rs. 12,000. The annual output of the company is Rs. 70,000. The annual output and manufacturing costs are directly proportional to the no. of machines. The shareholders get 12.5% of the total profit which is equal to the total output minus the total cost. If 7.14% of machines remain closed throughout the year, then the percentage decrease in the amount of profit of the shareholders would be:

Solution

Manufacturing cost (MC) of 14 machines = Rs. 42000
Output of 14 machines = Rs. 70000
Establishment cost (EC) = Rs. 12000
Profit = Rs.(70000 - 42000 - 12000) = Rs. 16000
Shareholder's profit = 12.5% of Rs. 16000 = Rs. 2000
It is given that 7.14% of the machines were non functional which means only 13 machines were functional.
MC of 13 machines = Rs. (42000 * $$\frac{13}{14}$$) = Rs. 39000 [As it is directly proportional to the number of functional machines]
Output of 13 machines = Rs. (70000 * $$\frac{13}{14}$$) = Rs. 65000 [As it is directly proportional to the number of functional machines]
EC of 13 machines = Rs. 12000 [As it does not depend on the number of functional machines]
Profit = Rs.(65000 - 39000 - 12000) = Rs. 14000
Shareholder's profit = 12.5% of Rs. 14000 = Rs. 1750
Reduction in Shareholder's profit = Rs.(2000 - 1750) = Rs. 250
Reduction % = $$\frac{250}{2000}$$*100% = 12.5%
Hence, option B is the correct answer.

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