Profit and Loss [लाभ और हानि]–08

Question: A milkman mixes water with milk and sells the mixture at the cost price of pure milk. The volume of water in liters to be mixed with each liter of milk to get a 25% profit is   [Ans. (a) 1/4]

(a) 1/4     (b) 1/5     (c) (1 ¾)    (d) can’t be determined  (e) None of these

Solution:

Detailed Explanation:

First method: Given that a milkman mixes water with milk and sells the mixture at the cost price of pure milk. Here, the price of water to be added is always taken as 0; since water is not bought. Also, given that the cost price of pure water is the selling price of the mixture.

Let the cost price of the mixture of water and milk is 100. Since the profit percent is 25, so the selling price of the mixture is 100+25 = 125. Since the selling price of the mixture is the cost price of pure water, so cost price of pure water is 125.

By the method of “Alligation”,

Ratio of quantity of water to the quantity of pure milk =125-100: 100-0 = 25: 100 = 1: 4  

Therefore, 1/4^th of liter of water should be added to each liter of the pure milk. Ans.

Second Method: W: M = profit %: 100 = 25:100 = 1:4

Therefore, 1/4^th of liter of water should be added to each liter of the pure milk. Ans.

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                                   Solution: First Method

                          By method of Alligation,

                     Water (Rs/kg)           Milk (Rs/kg)

                          0                            100+25    

                                    Mean (Rs/kg)                   

                                      100 (let)

                         25               :            100  

                     Or, 1              :                4  

Therefore, 1/4^th of liter of water should be added to each liter of the pure milk. Ans.