Question

A milkman has 15 liters of pure milk. how many liters of water have to be added to it so that he gets 60% profit by selling at cost price?
A.9 liters
B.10 liters
C.8 liters
D.12 liters

Answer 1

Hint: Here the cost price and selling price is the same but the milkman will sell the milk on 60% profit by adding some water to his pure milk. We have to find the amount of water he will add to make this much profit. We will use the given data to find the amount of water he adds.

Complete step-by-step answer:
Given is the 15 liters of pure milk.
Now consider he will add x liters of water to this milk.
The mixture is now 15+x liters.
But the selling price is the same as the cost price. But we are not given both the prices.
So we can say that he earned profit by adding water.
Let’s say 15 liters of milk is sold for Rs. 100
Now if he gains 60% profit then we will generally say that the amount earned will be 160.
But definitely the amount of milk has increased.
So using the unitary method we will find the amount of water added.
\[\begin{gathered}
  100 = 15 \\
  160 = ? \\
\end{gathered} \]
On cross multiplying we get,
\[? = \dfrac{{160 \times 15}}{{100}} = 24\]
Thus the mixture becomes 24 litres.
But as we know that the original pure milk is of 15 litres so the amount of water added will be,
\[24 - 15 = 9\] litres.
Thus he adds 9 litres of milk to his original pure milk.
Thus option A is correct.
So, the correct answer is “Option A”.

Note: Note that if he sells the pure milk directly at the same selling price and cost price he will neither gain nor lose but after adding water the quantity increases and now though he sells on cost price he is selling 9 liters more . so definitely he will gain some amount.