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  • Question
  • In what ratio should milk and water be mixed so that after selling the mixture at the cost price a profit of 50/3 % is made?


  • Options
  • A. 1:2
  • B. 6:1
  • C. 2:3
  • D. 2:5

  • Correct Answer
  • 6:1 

    Explanation

    Method 1 to solve the equation.
    Let us assume Cost Price (C.P) of 1 liter milk be Y rupees.
    According to question,
    Selling Price (S.P) of 1 liter of mixture Y rupees. (Selling price should be same as Cost price)
    Profit = 50/3 %
    Let us assume Cost price of 1 Liter of Mixture of Water and Milk = C
    Cost price of 1 Liter of Mixture of Water and Milk = Selling price of Mixture - Profit
    C = Y - C x 50/3%
    ? C = Y - C x 50/3x100
    ? C = Y - C x 1/3x2
    ? C = Y - C/6
    ? Y = C + C/6
    ? Y = (6C + C)/6
    ? Y = (6C + C)/6
    ? Y = 7C/6
    ? C = 6Y/7
    Since in Y rupees we will get 1 liter milk.
    Hence in 1 rupees we will get 1/Y liter milk.
    Hence in 6Y/7 rupees we will get 1 x 6Y/7 x Y liter milk.
    Hence in 6Y/7 rupees we will get 6/7 liter milk.
    We need 1 liter mixture of milk and water for sold on the same price, we need to mix the water.
    So water quantity in mixture = 1 - 6/7 = 1/7

    Ratio of Milk and water in mixture = quantity of Milk in Mixture/quantity of Water in Mixture
    Ratio of Milk and water in mixture = 6/7 / 1/7
    Ratio of Milk and water in mixture = 6 x 7 / 7
    Ratio of Milk and water in mixture = 6 / 1
    Ratio of Milk and water in mixture = 6 : 1

    Method 2 to solve the question.
    Let the original amount of milk be 1 liter and the cost price is 1 rupees per liter.
    Cost price of milk = 1 rupees.
    Selling price of Mixture = 1 rupees.
    When the milk is mix with x liters of water milk remaining is 1- x.
    Let us assume the cost price of milk in mixture is Y and given that the Sold Price is 1.
    we should use the Profit formula in algebra,

    Y + Y x 50/3 % = 1
    Y + Y x 50/3 x 100 = 1
    Y + Y x /3 x 2 = 1
    7Y/6 = 1
    Y = 6/7
    Y = 6/7 is the cost price of Mixture for 1 liter.
    Since water is free so there is not cost of water in mixture. So price of milk is 6/7 rs in mixture.
    Since as per question,
    In 1 rupees we will get 1 liter of milk.
    hence in 6/7 rupees we will get 1 x 6/7 = 6/7 liter of milk.
    Now we have to make 1 liter of mixture with water and milk.
    quantity of Water + Quantity of Milk = 1 liter
    quantity of Water + 6/7 = 1
    quantity of Water = 1 - 6/7 = (7 - 6)/7
    quantity of Water = 1/7
    Ratio of milk and Water = Quantity of Milk / quantity of Water
    Ratio of milk and Water = (6/7) / (1/7)
    Ratio of milk and Water = (6/7) x (7/1)
    Ratio of milk and Water = 6 x 7/ 7 x 1
    Ratio of milk and Water = 6 :1


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