A company has 12 machines of equal efficiency in its factory. The annual manufacturing expenses are Rs. 24,000 and the establishment charges are Rs. 10,000. The annual output of the company is Rs. 48,000. The annual output and manufacturing costs are directly proportional to the number of machines while the shareholders get the 10% profit, which is directly proportional to the annual output of the company. If 8.33% of machines remained close throughout the year. Then the percentage decrease in the amount of shareholders is:

(a) 16.66%

(b) 14.28%

(c) 8.33%

(d) None of these

**Ans**: (b) 14.28%

**Explanation**:

**1 ^{st} Case:**

No of machines = 12

Manufacturing cost = ₹ 24000

Establishment charge= ₹ 10000

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∴ Total cost = ₹34000

Output = ₹ 48000

Company profit = 48000 – 34000 = ₹ 14000

Profit by share holder = 14000 × 0.1 = ₹1400

**2 ^{nd} case:**

8.33\%=\displaystyle\frac{1}{12} \Rightarrow Now, 1 machine is less working in every 12 machines

So, no of machines = 11

Given that ,

Manufacturing cost \propto No of machines

And output \propto No of machines

For 1^{st} case, data were given for 12 machines, now those have to be recalculated for 11 machines using unitary method.

∴ Manufacturing cost = 11 × 2000 = ₹ 22000

Establishment charge = ₹ 10000 [this cost is fixed]

___________________________________________

∴ Total cost = 22000 + 10000 = ₹32000

Output = 11 × 4000 = ₹44000

Now, company profit = 44000 – 32000 = ₹ 12000

Profit by share holder = 12000 × .01 = ₹12000

For share holder profit reduced from ₹1400 to ₹1200

Hence, decrease in profit = \displaystyle\frac{200}{1400}\times 100 = 14.28\%

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AyaanIn 2nd case manufacturing cost and output is taken for 11 machines, but why establishment charge is same as 12 machines?

Team NJPNote that is is given in question that

The annual output and manufacturing costs are directly proportional to the number of machines. But nothing is mentioned about establishment charges. So we would assume it as constant. See, the company has set up all the 12 machines already, so the cost of establishment is fixed, it would increase only if new machines are introduced.AYAANOh!, I see. Now I have understood