Question

A milkman buys milk at Rs. $25$ per liter and adds $\dfrac{1}{4}$ of water to it and sells the mixture at Rs. $25$ per liter. His gain $\left( {in\% } \right)$ is:-
A) 25
B) 20
C) 30
D) 15

Answer 1

Hint: First we have to find the actual price of milk after adding the water into it. Then find the relevant equation showing the relation between cost price, selling price and gain. Then solve it and find the cost price of the mixture. Further apply the formula for percentage gain to get the gain value over it as an answer.

Complete step-by-step answer:
Let us suppose that the milkman buys $x$liters of milk at the cost of $25$Rs per liter.
Then total cost of the milk $25 \times x$ $ = 25x$
Since milkman is adding $\dfrac{1}{4}$ portion water in the milk. So, actual mixture (milk + water) will become,
Milk quantity in mixture + Water quantity in mixture
$
   \Rightarrow x + \dfrac{x}{4} \\
   \Rightarrow \dfrac{{4x + x}}{4} = \dfrac{{5x}}{4} \\
 $ ……(1)
Now, milkman is selling the above mixture at a price of Rs $25$.
So, we now calculate his total earning value as,
${\text{total earning = }}\dfrac{{5x}}{4} \times 25 = \dfrac{{125x}}{4}$ (from equation 1)
Value of ${\text{gain = total earning - total cost}}$
Substitute the values, in above equation, we get gain amount as
$
   \Rightarrow \dfrac{{125x}}{4} - 25x \\
   \Rightarrow \dfrac{{125x - 100x}}{4} \\
   \Rightarrow \dfrac{{25x}}{4} \\
 $
Gain amount = $\dfrac{{25x}}{4}$ ….(2)
And cost price = 25x
We know that gain percentage value, will be
Now, profit gain percentage$ = \dfrac{{gain \times 100}}{{C.P}}$
$ \Rightarrow \dfrac{{\dfrac{{25x}}{4}}}{{25x}} \times 100$ (from equations 1 and 2)
$ \Rightarrow $ gain percentage = 25

$\therefore $ His gain $\left( {in\% } \right)$ is 25%. So, option A is the correct answer..

Note: In such cases, profit and loss has to be calculated with the help of cost price and selling price. Knowledge of percentage value will always be needed in such problems. Always remember here that the cost of water will be taken zero in the mixture. So adding the water into milk will increase the quantity but not the cost price. Two important formulas are:
Percentage profit =$\dfrac{{selling\;price - \cos tprice}}{{\cos t\;price}} \times 100$
And percentage loss = $\dfrac{{\cos tprice - selling\;price}}{{\cos t\;price}} \times 100$