Question

By selling an article for $Rs.225$, the shopkeeper loses $25\% $. Find the $\% $gain or loss, if be article be sold for $Rs.360.$
$A)20\% $ gain
\[B)20\% \] loss
$C)10\% $ loss
$D)10\% $ gain

Answer 1

Hint: First, we have to see what is loss and gain.
Gain means we get the profit of the product that we sold from the original amount; like if I buy a cake for one rupee and sell it to someone for two rupees then my gain(profit) is one rupee.
Similarly, the loss is all about that we lost some money on the product inverse, like if I buy a cake for two rupees and sell it for one rupee then it must be considered as the loss of one rupee on the trade.
Formula used: $Gain = S.P - C.P$ where S.P is the selling price, and C.P is the cost price.
$Gain\% = \dfrac{{Gain}}{{C.P}} \times 100$

Complete step by step answer:
Let us assume the original price of the product is $Rs.100$(easy to calculate with the percentage) since the cost price is unknown, we assume that the cost price (if it is given then we may simply substitute that).
Since shopkeepers lose $25\% $ on the process of selling thus, we get $Rs.75$(cost price is $Rs.100$and losses $25\% $).
Thus, we have the selling and cost price that we assumed, now applying the values into the given selling price we get, selling an article for $Rs.225$ (where cost price is hundred and selling price is seventy-five).
Then the cost price from the given is $Rs.\dfrac{{100}}{{75}} \times 225$ (original cost price into which we assumed prices for the twenty-five percent).
Further solving we get, $Rs.\dfrac{{100}}{{75}} \times 225 \Rightarrow 1.333 \times 225 \Rightarrow 300$ is the cost price for the given question.
Hence, we have the cost price and selling price; since the cost price is $Rs.300$ and the sold for $Rs.360.$ Clearly, we see that there is a profit (read the hint for more clarification).
Hence the gain percent is calculated using $Gain = S.P - C.P \Rightarrow 360 - 300 = 60$ rupees (which is the gain).
But we need to calculate the percentage of the gain, thus we apply the percentage of gain formula we get, $Gain = \dfrac{{60}}{{300}} \times 100$ (sixty is the gain rupees, three hundred is the cost price).
Thus, we get, after solving $Gain = 20\% $

So, the correct answer is “Option A”.

Note: since we didn’t get the loss of the product and thus options\[B)20\% \] loss, $C)10\% $ the loss is eliminated.
Also, if the option $D)10\% $ gain is correct then we did not get the profit as $Rs.60$we only got the profit as $Rs.30$and thus it is also incorrect.
The formula for the loss percent is$Loss = C.P - S.P$, after finding the loss we will convert it into the loss percentage is same as above for the profit, the only difference is$Loss\% = \dfrac{{Loss}}{{C.P}} \times 100$.