Question

A retailer 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 $33.33$%. However, as it turned out, $50$% of the components were rejected. What is the loss to the manufacturer?

• A. $15$%
• B. $16.66$%
• C. $20$%
• D. $13.33$%

Answer 1

The correct option is B $16.66$%

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 $33.33\%$

We know that $SP=CP+Profit$

$\Rightarrow 400000=CP+33.33\%ofCP$

$\Rightarrow 400000=CP+\frac{CP}{3}=\frac{4\times CP}{3}$

$\therefore CP=\frac{400000\times 3}{4}=300000Rs$

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

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

$Loss=CP-SP=300000-250000=50000Rs$

$\therefore Losspercentage=\frac{Loss\times 100}{CP}=\frac{50000\times 100}{300000}=\frac{100}{6}=16.66\%$