Question : When an article is sold at a 5% discount, then there is a profit of 14%. If the discount is 11%, then what will be the profit?
Option 1: 7.6%
Option 2: 8.4%
Option 3: 7.2%
Option 4: 6.8%
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Correct Answer: 6.8%
Solution :
Given: When an article is sold at a 5% discount, then there is a profit of 14%.
Use the formulas,
SP = MP – Discount
CP = $\frac{100}{100+\text{Profit percent}}\times SP$
Profit percentage = $\frac{SP–CP}{CP}\times 100$
Where SP, CP, and MP are the selling price, cost price, and the marked price.
Let the MP of an article be INR 100.
Discount = 5%
⇒ SP = INR 100 – INR 5 = INR 95
Profit percentage = 14%
⇒ CP = INR $\frac{100}{100+14}\times 95$
⇒ CP = INR $\frac{100}{114}\times 95=$ INR 83.3
For the discount of 11%,
⇒ SP = INR 100 – INR 11 = INR 89
Profit percentage $=\frac{89–83.3}{83.3}\times 100$
$=\frac{5.7}{83.3}\times 100=$ 6.8%
Hence, the correct answer is 6.8%.
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