Question : By selling a table for INR 1,596, Aarav loses 24%. At what price (in INR) should he sell it to gain 24%?
Option 1: 3,196
Option 2: 3,024
Option 3: 1,979
Option 4: 2,604
Correct Answer: 2,604
Solution :
Given: By selling a table for INR 1,596, Aarav loses 24%.
Use the formulas,
Profit percentage = $\frac{\text{SP–CP}}{\text{CP}}\times 100$,
Loss percentage = $\frac{\text{CP–SP}}{\text{CP}}\times 100$,
where $SP$ and $CP$ are the selling price and the cost price.
$24 = \frac{\text{CP–1596}}{\text{CP}}\times 100$
⇒ $24 CP = 100 CP-159600$
⇒ $76 CP =159600$
⇒ $ CP= $ INR 2,100
Now, $24= \frac{\text{SP–2100}}{2100}\times 100$
⇒ $504= SP-2100$
⇒ $SP=2100+504$
⇒ $ SP= $ INR 2,604
Hence, the correct answer is INR 2,604.
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