Question & Answer
QUESTION

Every year before the festive season, a brand store increases the price of the product by 42% and then produces two successive discounts of 10% and 11% respectively. What is the percentage loss and percentage gain?

ANSWER Verified Verified
Hint: Here, first we have to assume that the CP is Rs.100 and then we have to calculate the SP if the CP is increased by 42% which is 100 + 42%. Next, we have to calculate the SP for 10% discount and the SP for 11% discount. Now, the SP will be greater than the CP so we will have a gain and then calculate the gain% by the formula:
$Gain=\dfrac{Gain}{CP}\times 100$

Complete Step-by-Step solution:
Here, given that a brand store increases the product of the price by 42% with two successive discounts of 10% and 11%.
Now, we have to calculate the loss% or gain%.
First let us assume that the cost price of the brand be, CP = Rs.100.
Now, the shopkeeper sells by increasing the price to 42%,
$\begin{align}
  & SP=100+\dfrac{42}{100}\times 100 \\
 & SP=\text{ }100\text{ }+\text{ }42 \\
 & SP=142 \\
\end{align}$
 Now, we have to calculate SP for a 10% discount.
10% discount in SP = $SP\times Discount%$
10% discount in SP =$142\times \dfrac{10}{100}$
Now, by cancellation we get:
10% discount in SP = $142\times \dfrac{1}{10}$
10% discount in SP = $14.2$
Therefore, the first SP = SP – 10% discount in SP
SP = 142 – 14.2
SP = 127.8
Now, we have to calculate the SP for an 11% discount.
11% discount in SP = $SP\times Discount%$
11% discount in SP = $127.8\times \dfrac{11}{100}$
11% discount in SP = $1.278\times 11$
11% discount in SP =14.058
Now, the second SP = SP - 11% discount in SP
SP = 127.8 – 14.058
SP = 113.742
Therefore, we can say that,
CP = 100, SP = 113.742
Since, SP > CP the brand store has a gain.
Next, we have to calculate the gain%.
For that first we have to calculate gain.
Gain = SP – CP
Gain = 113.742-100
Gain = 13.742
Now we have to calculate gain%.
$
  Gain\%=\dfrac{Gain}{CP}\times 100 $
 $ Gain\%=\dfrac{13.742}{100}\times 100 $
 $ Gain\%\text{ }=\text{ }13.742% \\
$
Hence, we can say that the percentage of gain is 13.742%.

Note: In case if CP is not given you have to take it as Rs.100 for that amount you have to find SP and discount respectively. Also don’t forget that if SP > CP you have to calculate gain. If SP < CP then you will have to calculate loss.