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Normally commercial milk should be sold at Rs 36/liter which contains 90% milk and 10% water. A milkman who dishonestly sells 80% milk mixture as commercial milk in a cylindrical vessel that is supposed to be 5 cm in radius and 7 cm tall. The vessel is also tampered that the radius is reduced to 4 cm. If he sold the milk, he would have got 20% profit. What is the profit (in %) he obtained after cheating?

Normally commercial milk should be sold at Rs 36/liter which contains 90% milk and 10% water. A milkman who dishonestly sells 80% milk mixture as commercial milk in a cylindrical vessel that is supposed to be 5 cm in radius and 7 cm tall. The vessel is also tampered that the radius is reduced to 4 cm. If he sold the milk, he would have got 20% profit. What is the profit (in %) he obtained after cheating? Correct Answer 4 7/16

By selling dishonestly he would have got 20% profit

Cost price for 90% milk = 36 × 100/ (100 + profit%)

⇒ 36 × 100/(100 + 20)

⇒ Rs. 30

Cost of 80% milk = 30/9 × 8

⇒ Rs. 80/3

Volume of original vessel = π r2 h

⇒ 22/7 × 52 × 7

⇒ 550 cm3

Volume of tampered vessel = 22/7 × 42 × 7

⇒ 352 cm3

∴ Profit% = (Selling price of 550 cm3 – Cost price of 352 cm3)/(Cost price of 352 cm3) × 100

⇒ (550 × 36/1000 – 80/3 × 352/1000)/(80/3 × 352/1000) × 100

⇒ (781/75)/(704/3) × 100

⇒ 4 7/16%

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