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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