The marked price of a wooden frame is Rs. 900. A discount is offered on this frame. Accidentally, the cashier applied the discount twice while making the bill. As a result, it was sold at a price of Rs. 576. Still, a profit of 20% is earned. Had the cashier applied discount only once, what would have been the percent profit?
Solution
Correct Answer: Option C
On understanding the question statement properly, we observe that we are given selling price and profit percentage, and cost price can be easily found out with this information.
We know, Selling Price = Cost Price × (1 + (Profit %)/100)
⇒ Cost price of frame = Rs. 576/(1 + (20/100)) = Rs. 576/1.2 = Rs. 480
Now, let’s assume that the discount available is D%.
Since the cashier applied the discount twice accidentally, the selling price after 2 successive discounts = Marked price × (1 – (Discount %)/100) × (1 – (Discount %)/100)
⇒ 900 × (1 – D/100)2 = 576
⇒ 576/900 = (1 – D/100)2
⇒ 1 – D/100 = 24/30 = 0.8
⇒ D = 20
Hence, the available discount is 20%.
Has the cashier applied the discount correctly,
Selling price = 900 × (1 – 20/100) = 900 × 0.8 = Rs. 720
In this case, % profit = (720 – 480)/480 × 100 = 50
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