Question

A manufacturer undertakes to supply $5000$ pieces of particular component at Rs. $100$ per piece. According to his estimates, even if $20$% fail to pass the quality tests, then he will make a profit of $20$%. However, as it turned out, $50$% of the components were rejected.

What is the loss to the manufacturer ?

• A. $25$%
• B. $15$%
• C. $35$%
• D. $5$%

Answer 1

The correct option is A $25$%

Total components $=5000$

If 20% fails, then remaining components to be sold $=5000-20\%of5000=4000$

Selling price of a component $=100Rs.$

$\therefore TotalSellingPrice=100\times 4000=4,00,000Rs$

Since, after selling $4000$ components, retailer makes a profit of $20$

We know that $SP=CP+Profit$

$\Rightarrow 400000=CP+20\%ofCP$

$\Rightarrow 400000=CP+\frac{CP}{5}=\frac{6\times CP}{5}$

$\therefore CP=\frac{400000\times 5}{6}=\frac{1000000}{3}Rs$

Now, when $50\%$ components rejected, then number of components to be sold = $=5000-50\%of5000=2500$

$TotalSellingPrice\left(SP\right)=25000\times 100=250000Rs$

$Loss=CP-SP=\frac{1000000}{3}-250000=\frac{250000}{3}Rs$

$\therefore Losspercentage=\frac{Loss\times 100}{CP}=\frac{\frac{250000}{3}\times 100}{\frac{1000000}{3}}=25\%$