Question

A milkman has 20 litres of milk. If he mixes 5 litres of water, which is freely available, in 20 litres of pure milk. If the cost of pure milk is Rs. 18 per litre, then the profit of the milkman, when it sells all the mixture at cost price, is:
(a) 20%
(b) 25%
(c) 33.33%
(d) 18%

Answer 1

Hint: Start by finding the cost price of the mixture of milk using the data that Rs. 18 is the cost price of pure milk and water is free of cost. On doing so the total cost comes out to be $ 18\times 20=Rs.\text{ 360} $ . Now as the milkman mixed water, the total amount he has for selling is 25 litres. Find the amount earned by selling this 25 litres. Find the difference of the two results, and the difference is the profit. Find its % with respect to total costing and report the answer.

Complete step-by-step answer:
Let us start by finding the cost price of the mixture using the point that the cost price of pure milk is Rs. 18 and there is a total of 20 litres of milk and water is free.
$\text{CP}=18\times 20+5\times 0=Rs.\text{ 360}$
Now the amount of impure milk the milkman has is 25 litres. He sells each litre of impure milk for the same amount as the CP of one litre of milk, i.e. Rs. 18. So, his total earning is:
$Earned=18\times 25=Rs.\text{ 450}$
So, if we subtract the amount earned from the amount he paid as the cost, we get the profit. So, the profit is: 450-360= Rs. 90.
Now we need to find the % profit. To find the percentage of Rs. 90 with respect to total costing, i.e., Rs. 360, we will divide 90 by 360 and multiply the result by 100. On doing so, we get
$\text{Percent profit}=\dfrac{90}{360}\times 100=25\%$
So, the correct answer is “Option B”.

Note: Don’t get confused and find the % profit with respect to selling price , as you should be very clear that the percentage loss or profit are terms related to the actual pricing not to the price for which you crack the deal. The other way of thinking of this is selling price might vary from buyer to buyer depending on the bargain they put in but the costing is always constant.