2 TIPS on cracking Aptitude Questions on Percentages

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Tip #1: Formula for change Percentage change= {[New Value – Original Value]/ Original value} x 100%

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%

Note: The most common type of questions on percentage that are encountered in any aptitude type paper is the Change Type, i.e., you will be required to calculate the percentage of change in any quantity, be it the price, population, or simply the amount of rainfall. It is imperative to remember that under all circumstances, the denominator will be the original value.

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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

Notes: Let the price of an item be first reduced by the X%, then increased by y% and then finally increased by another y%. In order to solve the problem, first consider the initial price to be P. Then calculate the first discounted price. Let it be Q. Calculate the raised price by operating upon Q. Calling this new price to be RR, calculate the final price by raising R by y%.

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