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A milkman purchased 10 litres of milk at rupees 7 per litre and forms a mixture by adding freely available water which constitutes 16.66 % of mixture later on he replaced the mixture by some freely available water and thus the ratio of milk is to water is 2:1 he then sold the new mixture at cost price of milk and replaced amount of mixture at twice the cost of milk then. what is the profit percentage?
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Problem Statement

A milkman purchased 10 litres of milk at rupees 7 per litre and forms a mixture by adding freely available water which constitutes 16.66 % of mixture later on he replaced the mixture by some freely available water and thus the ratio of milk is to water is 2:1 he then sold the new mixture at cost price of milk and replaced amount of mixture at twice the cost of milk then. what is the profit percentage? Explain in details.


Solution


Step 1: Initial Mixture

Initial Cost price of 10 litres of milk = 10 * 7 = 70

Let the amount of water added be x litres

Then, the amount of mixture = 10 + x litres

16.66% of the mixture is water. Hence,

x = (16.66/100) * (10 + x)

100x = 166.6 + 16.66x

83.34x = 166.6

x = 2 litres

Therefore, amount of water added = 2 litres and amount of milk = 10 litres

Hence, the initial mixture contains 10 litres of milk and 2 litres of water.


Step 2: Final Mixture

Let the amount of mixture replaced be y litres

Amount of milk in the mixture replaced = (2/3) * y litres

Amount of water in the mixture replaced = (1/3) * y litres

Amount of milk left in the mixture = 10 - (2/3) * y litres

Amount of water left in the mixture = 2 - (1/3) * y litres

Let the amount of water added be z litres

Then, the amount of mixture = 10 - (2/3) * y + z litres

Also, the ratio of milk to water in the final mixture is 2:1.

Therefore,

(10 - (2/3) * y)/(2 - (1/3) * y + z) = 2/1

10 - (2/3) * y = 4 - (2/3) * y + 2z

2z = (2/3) * y + 6

z = (1/3) * y + 3


Step 3: Calculation of Profit Percentage

The final mixture is sold at cost price of milk. Therefore, selling price of 1 litre of mixture = selling price of 1 litre of milk = Rs. 7

Cost price of 1 litre of initial mixture = 70/12 = Rs. 5.83

Cost price of 1 litre of final mixture = (10 - (2/3) * y + z)/(10 - (2/3) * y + z + y
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A milkman purchased 10 litres of milk at rupees 7 per litre and forms a mixture by adding freely available water which constitutes 16.66 % of mixture later on he replaced the mixture by some freely available water and thus the ratio of milk is to water is 2:1 he then sold the new mixture at cost price of milk and replaced amount of mixture at twice the cost of milk then. what is the profit percentage?
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A milkman purchased 10 litres of milk at rupees 7 per litre and forms a mixture by adding freely available water which constitutes 16.66 % of mixture later on he replaced the mixture by some freely available water and thus the ratio of milk is to water is 2:1 he then sold the new mixture at cost price of milk and replaced amount of mixture at twice the cost of milk then. what is the profit percentage? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A milkman purchased 10 litres of milk at rupees 7 per litre and forms a mixture by adding freely available water which constitutes 16.66 % of mixture later on he replaced the mixture by some freely available water and thus the ratio of milk is to water is 2:1 he then sold the new mixture at cost price of milk and replaced amount of mixture at twice the cost of milk then. what is the profit percentage? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A milkman purchased 10 litres of milk at rupees 7 per litre and forms a mixture by adding freely available water which constitutes 16.66 % of mixture later on he replaced the mixture by some freely available water and thus the ratio of milk is to water is 2:1 he then sold the new mixture at cost price of milk and replaced amount of mixture at twice the cost of milk then. what is the profit percentage?.
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