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?
- Rs. 12,000
- Rs. 13,000
- Rs. 14,000
- 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.
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?