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
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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.