Question

A dairyman pays Rs. 6.40 per litre of milk. He adds water and sells the mixture at Rs. 8 per litre thereby making 37.5% profit. The proportion of water to milk received by the customer is
A. 1:10
B. 1:12
C. 1:15
D. 1:20

Answer 1

Hint: et the quantity of milk be x litres and quantity of water added be y litres. The dairyman makes 37.5% profit by selling the water mixed milk at Rs. 8 per litre. $ 6.40x $ will be the cost price (CP) and $ 8\left( {x + y} \right) $ will be the selling price (SP) and the profit is 37.5%. Using the relation between CP, SP and profit find the ratio of quantities of water and milk.
 $ Profit = \dfrac{{\left( {SP - CP} \right)}}{{CP}} \times 100 $ , where SP is the selling price and CP is the cost price.

Complete step-by-step answer:
We are given that a dairyman pays Rs. 6.40 per litre of milk. He adds water and sells the mixture at Rs. 8 per litre thereby making 37.5% profit.
We have to find the proportion of water to milk received by the customer.
Let the quantity of milk be x and quantity of water mixed in the milk be y.
The cost price of one litre of milk is $ 6.4litr{e^{ - 1}} \times xlitre = 6.4x $
The selling price of one litre of milk and water is $ 8litr{e^{ - 1}} \times \left( {x + y} \right)litre = 8\left( {x + y} \right) $
The profit generated is 37.5%.
 $ Profit = \dfrac{{\left( {SP - CP} \right)}}{{CP}} \times 100 $
On substituting the values, we get
 $
  37.5 = \dfrac{{8\left( {x + y} \right) - 6.4x}}{{6.4x}} \times 100 \\
   \Rightarrow \dfrac{{8x + 8y - 6.4x}}{{6.4x}} = \dfrac{{37.5}}{{100}} \\
   \Rightarrow 1.6x + 8y = 0.375 \times 6.4x \\
   \Rightarrow 1.6x + 8y = 2.4x \\
   \Rightarrow 8y = 2.4x - 1.6x \\
   \Rightarrow 8y = 0.8x \\
   \Rightarrow 8y = \dfrac{8}{{10}}x \\
   \Rightarrow 80y = 8x \\
   \Rightarrow \dfrac{y}{x} = \dfrac{8}{{80}} \\
  \therefore \dfrac{y}{x} = \dfrac{1}{{10}} = 1:10 \\
 $
Therefore, the ratio of quantities (proportion) of water to milk received by the customer is 1:10.

So, the correct answer is “Option A”.

Note: Here after substituting all the values of SP, CP and profit, we got a linear equation in 2 variables. An easy method to solve the linear equations is to put all the similar terms together and the terms which contain variables on the left hand side. Cost price is the price at which an item is purchased and selling price is the price at which that item is sold.