HAT percentages: choose the base before calculating

Find the base

p% means p/100. If 30% of a class is absent, the base is the whole class. If a new price is 30% higher than an old price, the base for that increase is the old price.

For example, 35% of a number is 147. The whole is 147 ÷ 0.35 = 420. To find 60% of the same number, calculate 0.60 × 420 = 252. Multiplying 147 by 0.60 would use the part as the base.

Percentage change

A fee rises from Rs. 500 to Rs. 575. The change is 75, and 75 ÷ 500 × 100 = 15%. Dividing by 575 answers a different question: the difference as a percentage of the new fee.

Estimate before calculating. A 75-unit rise on 500 is a little less than one sixth, so a result near 15% is plausible; 75% is not.

Reverse a percentage

After a 20% discount, a bag costs Rs. 960. The remaining price is 80% of the original, so 0.80 × original = 960. Divide: original = Rs. 1,200.

Adding 20% to 960 produces 1,152, not 1,200. The added percentage would be based on the discounted price, whereas the original discount was based on the original price.

Successive changes

Convert each change into a multiplier. A 10% increase is ×1.10; a 10% decrease is ×0.90. Apply them in order: 1.10 × 0.90 = 0.99, so the final amount is 99% of the original: a 1% decrease.

Two reductions of 10% and 20% produce 0.90 × 0.80 = 0.72 of the original, a 28% overall reduction. Adding the reductions to get 30% overlooks the new base after the first reduction.

Percentage points and percent

An accuracy rate rises from 40% to 50%. That is an increase of 10 percentage points. Relative to the original rate, the increase is 10 ÷ 40 × 100 = 25%. Read which comparison the question requests.

Try these before opening the answers

Continue with quantitative practice →