Question : A manufacturer marked an item at INR 75 and sold it allowing a 14% discount. If his profit was 29%, then the cost price (in INR) of the item was:
Option 1: 64
Option 2: 57
Option 3: 45
Option 4: 50
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Correct Answer: 50
Solution :
Let's denote the cost price of the item as $C$.
The item was marked at INR 75, and a 14% discount was given.
⇒ The selling price (SP) is 86% of the marked price.
⇒ $SP=0.86×\text{Marked Price}$
⇒ $SP=0.86×75$
Now, the profit percentage (P) is given by the formula:
P $=\frac{\text{Selling Price−Cost Price}}{\text{Cost Price}}×100$
In this case, the profit percentage is 29%,
⇒ $29=\frac{(0.86×75)−C}{C}×100$
⇒ $29=\frac{64.5−C}{C}×100$
⇒ $29C=6450−100C$
⇒ $129C=6450$
⇒ $C=\frac{6450}{129}$
⇒ $C=50$
Hence, the correct answer is 50.
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