Profit and Loss : Manufacturer

Question

A manufacturer undertakes to supply 2000 pieces of a particular component at Rs.25 per piece. According to its estimates, even if 5% fail to pass the quality tests, then he will make a profit of 25%.

However, as it turned out, 50% of the components were rejected.

What is the loss to the manufacturer?

1. Rs. 12,000
2. Rs. 13,000
3. Rs. 14,000
4. Rs. 15,000

If possible try to explain your steps, as I have tried to solve this question several times. But failed to solve it.

Answer 1

Let's denote the cost to make the components as $C$ rupees.

With a $5\%$ failure rate, the revenue will be $(2000\times 0.95)\times 25$ rupees. If this represents a $25\%$ profit, we have $$((2000\times 0.95)\times 25)=1.25C$$ Now we can work out $C$, which is $C=38000$. However, $50\%$ of the components were rejected, so only $1000$ was sold at $25$ rupees, earning a revenue of only $25000$ rupees. Based on the value of $C$, can you work out how much loss was made?