Question

A shopkeeper reduces the price of his goods by $50$% at the time of sale. Initially the price was fixed to get a profit of $20$% on selling price after allowing $15$% cash discount. His approx % of profit or loss?

• A. $26.5$ % loss
• B. $31$ % loss
• C. $29.5$ % loss
• D. $31.5$ % loss

Answer 1

Answer: (A)

$26.5$ % loss

Let Initial price of goods $=xRs$

Discount = 15%

So, $Sellingprice=Markedprice-Discount$

$=x-15\%ofx=\frac{17x}{20}$

Given that this selling price will give profit of 20% on selling price.

So, $Profit=20\%of\frac{17x}{20}=\frac{17x}{100}$

Hence, Cost Price (CP) $=Sellingprice-Profit=\frac{17x}{20}-\frac{17x}{100}=\frac{68x}{100}$

When Shopkeeper reduces price of goods by 50%

Then Selling price (SP) $=x-50\%ofx=\frac{x}{2}=\frac{50x}{100}$

Since Selling Price < Cost Price. So, there is a loss.

Hence, $Loss=CP-SP=\frac{68x}{100}-\frac{50x}{100}=\frac{18x}{100}$

So, $Losspercentage=\frac{Loss\times 100}{CP}=\frac{\frac{18x}{100}\times 100}{\frac{68x}{100}}=\frac{1800}{68}=26.47=26.5\%\left(Approx\right)$