Percentage shortcuts for aptitude tests

Work out percentages in your head with the 10% and 1% method, fraction equivalents, reverse percentages and successive changes, with worked examples.

Percentages show up everywhere in aptitude tests: in direct questions, in profit and loss, in discounts, in data interpretation and in interest. The good news is that almost all of them use the same few ideas. Once these feel natural, most percentage questions take seconds instead of minutes.

Start from 10% and 1%

10% of a number is the number divided by 10. 1% is the number divided by 100. Almost every other percentage can be built from these two.

Example: 35% of 640.

• 10% of 640 = 64, so 30% = 192.
• 5% is half of 10%, so 5% = 32.
• 35% = 192 + 32 = 224.

The same idea works for awkward percentages. 19% is 20% minus 1%: 19% of 300 = 60 − 3 = 57.

Learn the fraction equivalents

Many percentages are simple fractions. Using the fraction is often faster than multiplying.

Example: 12.5% of 488 is 488 ÷ 8 = 61.

Swap the numbers

x% of y is always equal to y% of x, because both are x × y ÷ 100. Use whichever is easier.

Example: 48% of 25 looks awkward, but 25% of 48 is a quarter of 48 = 12.

Reverse percentages: find the whole

Many questions give you the part and ask for the whole. If a part P is r% of the whole, then:

Whole = P × 100 ÷ r

Example: A student needs 35% to pass. She scored 188 and missed by 22 marks. What is the maximum mark?

• The pass mark is 188 + 22 = 210.
• 210 is 35% of the maximum, so the maximum is 210 × 100 ÷ 35 = 600.

A common trap is the "price after a rise" question. If a price rises by 20% to ₹960, the original price is not ₹960 − 20% of 960. It is 960 × 100 ÷ 120 = ₹800, because ₹960 is 120% of the original.

Percentage change

Change % = (new − old) ÷ old × 100

Always divide by the old value. A rise from 50 to 60 is a 20% rise, but a fall from 60 back to 50 is only a 16⅔% fall, because the base has changed.

Successive changes

When one percentage change follows another, you can't simply add them. For changes of a% and b% (use negative numbers for decreases), the overall change is:

a + b + (a × b ÷ 100) %

Example: A price rises by 20% and then falls by 20%.

• Overall change = 20 + (−20) + (20 × −20 ÷ 100) = −4.
• So the price ends up 4% lower than it started, not back where it began.

The same rule covers two discounts. A 20% discount followed by a 10% discount is −20 − 10 + (200 ÷ 100) = −28, a single discount of 28%, not 30%.

Check your answer quickly

• Is the answer the right size? 35% of 640 should be a bit more than a third of 640, so roughly 210 to 230.
• For reverse questions, put your answer back in: 35% of 600 is 210. ✓
• If two options are close, recheck which value you divided by.

Practise

The best way to make these shortcuts automatic is to use them under a little time pressure. Try the solved percentage examples, then the profit and loss and discount pages, which use exactly the same ideas.

Practise it: solved examples.