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Tip #1: Formula for change: Percentage change= [New Value – Original Value] x 100% Original value Question: A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation? Solution: Expected correct answer = 5/3 x Number The new erroneous answer = 3/5 x Number Percentage error = [3/5 – 5/3]/ 5/3 = - 64% Question: If Sham had 24 shirts originally, by what % were his shirts reduced if he donated 4 of them? Solution: Percentage by which his shirts were reduced =(4 / 24) x 100%= 16.6%
Tip #2: Questions that involve series of changes should be solved step by step Question: By what % the new price of wardrobe has to be increased to get original value, if it was decreased by 20% ? Solution: Let the original price be X. Then the new price= (100 – 20)% of X= 80% of X= 0.8 X Required raise in price= X – 0.8X= 0.2X Percentage change in price= (0.2X / 0.8X) x 100%= 25% Question: Ram buys good worth Rs. 500. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods. Solution: Price after rebate= 94% of Rs. 500 = 0.94 x 500 Sales tax= 10% of rebated price. Final price= 110% of price after rebate= 1.1 x 0.94 x 500 = Rs. 517
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