Question : A shopkeeper marks an article at such a price that after giving a discount of $12 \frac{1}{2} \%$ on the marked price, he still earns a profit of 15%. If the cost price of the article is Rs. 385, then the sum of the marked price and the selling price (in Rs.) of the article is:
Option 1: 948.75
Option 2: 849.5
Option 3: 984.75
Option 4: 954.75
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Correct Answer: 948.75
Solution :
Let the marked price as MP and the selling price as SP.
Given that the shopkeeper earns a profit of 15%, the selling price SP is 115% of the cost price.
⇒ SP = 1.15 × CP = 1.15 × 385 = Rs. 442.75
Also, given that the shopkeeper gives a discount of $12 \frac{1}{2} \%$ on the marked price, the selling price SP is 87.5% of the marked price.
⇒ SP = 0.875 × MP
Substituting `SP` from the first equation into the second equation,
⇒ 442.75 = 0.875 × MP
⇒ MP = $\frac{442.75}{0.875}$ = Rs. 506
Therefore, the sum of the marked price and the selling price,
⇒ MP + SP = 506 + 442.75 = Rs. 948.75
Hence, the correct answer is 948.75.
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