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A greedy shopkeeper marked the price of his goods to 20% above the cost price and gives a discount of 10%. He uses a faulty balance which measures 100 grams more than the actual weight. If he gains a profit of Rs. 1.8/kg then the cost price of 1 kg of sugar is:1. Rs. 1002. Rs. 203. Rs. 504. Rs. 10 |
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Answer» Correct Answer - Option 4 : Rs. 10 Given: Mark up = 20% Discount = 10% Measure 100 grams more Profit = Rs. 1.8/kg Formula Used: Marked price = Cost price × (100 + mark up%)/100 Selling price = Marked price × (100 - discount%)/100 Profit = SP - CP Calculation: Let the cost price of 1 kg of sugar be Rs. x He uses a faulty balance which reads 100 grams more than actual weight Instead of 1 kg he sells only 900 grams Cost price of 900 grams of sugar = Rs. (900/1000) × x ⇒ Rs. 0.9x He marked the price to 20% Marked Price of 1 kg sugar = Cost price × (100 + mark up%)/100 ⇒ x × (100 + 20)/100 ⇒ Rs. 1.2x He gives a discount of 10% Selling price of 1 kg sugar = Marked price × (100 - discount%)/100 ⇒ 1.2x × (100 - 10)/100 ⇒ Rs. 1.08x Profit = SP - CP ⇒ 1.8 = 1.08x - 0.9x ⇒ 0.18x = 1.8 ⇒ x = 10 ∴ Cost price of 1 kg of sugar is Rs. 10. |
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