Every year, before festive season,a shopkeeper increases the price of the product by 30% and then introduces two successive discounts of 15% and 20% respectively.What is the percentage loss and percentage gain?14%15%14.3%16%
Question
Every year, before festive season,a shopkeeper increases the price of the product by 30% and then introduces two successive discounts of 15% and 20% respectively.What is the percentage loss and percentage gain?14%15%14.3%16%
Solution 1
Let's solve this step by step:
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Let's assume the original price of the product is $100.
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Before the festive season, the shopkeeper increases the price by 30%. So, the new price becomes 30 = $130.
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Then, he introduces a discount of 15%. So, the price after the first discount becomes 130*(15/100) = $110.5.
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After that, he introduces another discount of 20%. So, the price after the second discount becomes 110.5*(20/100) = $88.4.
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Now, let's calculate the percentage loss. The formula for percentage loss is (Original Price - Final Price) / Original Price * 100. Substituting the given values, we get (100 - 88.4) / 100 * 100 = 11.6%.
So, the shopkeeper has a percentage loss of 11.6%. There is no percentage gain in this case as the final price is less than the original price. Therefore, none of the options provided (14%, 15%, 14.3%, 16%) are correct.
Solution 2
Let's assume the original price of the product is $100.
Step 1: Increase the price by 30% The new price becomes 100 = $130.
Step 2: Introduce a discount of 15% The price now becomes 130 = $110.5.
Step 3: Introduce a further discount of 20% The final price now becomes 110.5 = $88.4.
Now, let's calculate the percentage loss and gain:
Percentage loss = [(Original price - Final price) / Original price] * 100 Percentage loss = [(88.4) / $100] * 100 = 11.6%
Since the final price is less than the original price, there is no percentage gain. So, the percentage gain is 0%.
Therefore, none of the options provided (14%, 15%, 14.3%, 16%) are correct. The percentage loss is 11.6% and the percentage gain is 0%.
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