Question

The price of milk decreases by $20\%$. If a housewife wants to spend the same amount of money, how much percentage excess milk will she get?
(a) $16\dfrac{2}{3}\%$
(b) $25\%$
(c) $20\%$
(d) $50\%$

Answer 1

Hint: Let us assume that the cost price (C.P.) of 1 litre milk is equal to Rs. x. Now, the price of milk has decreased by $20\%$ so find the new decreased cost price which is the subtraction of x with $20\%$ of x. Now, we get the new cost price per litre of the milk. Now, find the amount of milk that can be got from Rs. x. As we know the new cost price can give 1 litre milk so by unitary method find the amount of milk for Re. 1 and then for Rs. x. In this way, we will get the new amount of milk which Rs. x can purchase. Now, find the percentage change of the new amount of milk from 1 litre.

Complete step by step answer:
Let us assume the C.P. of 1 litre milk is equal to Rs. x.
It is given that the price of the milk is decreased by $20\%$ so the new cost price is calculated by first of all finding $20\%$ of x and then subtracting the result of this percentage decrease from x.
$20\%$ of x is calculated by dividing 20 by 100 and then multiplying by x.
$\begin{align}
  & \dfrac{20}{100}x \\
 & \dfrac{x}{5} \\
\end{align}$
Now, subtracting the above result from x we get,
$x-\dfrac{x}{5}$
Taking x as common in the above expression we get,
$\begin{align}
  & x\left( 1-\dfrac{1}{5} \right) \\
 & =x\left( \dfrac{4}{5} \right) \\
\end{align}$
Hence, we got the decreased price for 1 litre milk as $Rs.\dfrac{4x}{5}$.
Now, $Rs.\dfrac{4x}{5}$ can purchase us 1 litre of the milk so by unitary method we can find how much milk we can get from Re. 1 by dividing 1 by $\dfrac{4x}{5}$.
Amount of milk that we can buy from Re. 1 is equal to:
$\dfrac{1}{\dfrac{4x}{5}}=\dfrac{5}{4x}$
Now, we have to find how much milk Rs. x can give which we are going to find by multiplying the above expression by x.
$\begin{align}
  & \dfrac{5}{4x}\left( x \right) \\
 & =\dfrac{5}{4} \\
\end{align}$
Hence, after the fallen cost price of 1 litre milk, Rs. x can give $\dfrac{5}{4}$ litres of milk.
The excess percentage of the amount of milk is calculated by taking the difference of $\dfrac{5}{4}$ litres and 1 litre and then divide this difference by 1 followed by multiplication will 100 we get,
$\begin{align}
  & \dfrac{\dfrac{5}{4}-1}{1}\times 100 \\
 & =\dfrac{5-4}{4}\times 100 \\
 & =\dfrac{1}{4}\times 100 \\
 & =25\% \\
\end{align}$
Hence, $25\%$ is the excess milk that the woman is getting after the decrement in cost price per litre of the milk.

So, the correct answer is “Option B”.

Note: A general confusion which you might also encounter in this problem is that it is given in this problem that in this statement “The price of milk decreases by $20\%$”, you might get confused “decreases by” in this statement with “decreases to” both these statements have different meanings.
In the below, we are giving the clear picture of what these two statements mean:
“decreases by” is the difference of new from the original or vice versa. For e.g. in this problem, it is given that the cost price of milk decreases by $20\%$. This means the initial cost price of milk and the final cost price of the milk has a difference of $20\%$.
Whereas “decreases to” means that the old price has changed and the number after decreases to will give the new price. For e.g. in this statement “the price of milk decreases to Rs 50” says that as the price is lower than the original price and the new price is equal to Rs. 50.