Aptitude · Percentages · Comparison

Asking 'more' takes the smaller base. Asking 'less' takes the larger.

“A is what per cent more than B” and “B is what per cent less than A” describe the same two numbers and have different answers. The numerator is always the difference; the whole question is which value goes underneath.

Set two values and switch the phrasing →

Top is always the difference. Bottom is the smaller value when asking MORE and the larger when asking LESS.

01 The idea

The inverse rule, and why it feels backwards

Ninety is what per cent more than eighty? The difference is 10, and the question asks “more than 80”, so 80 is the base: 10/80 = 12.5%. Now turn it around. Eighty is what per cent less than ninety? The difference is still 10, but the base is now 90: 10/90 = 11.11%.

Same pair, two answers, and neither is wrong. The comparison is always measured against the thing you are comparing to, which is whatever follows “than”. So the rule is mechanical: asking MORE puts the smaller value underneath, asking LESS puts the larger one there.

That inversion is what makes it feel backwards, and it is worth having as a phrase: more takes less, less takes more. If a question asks how much more A is, you divide by the smaller; if it asks how much less B is, you divide by the larger.

The other habit that transforms this topic is simplifying first. “1620 is what per cent more than 1440?” looks like long division. Reduce the pair to 9 : 8 and the difference is 1 part on a base of 8, which is 1/8 = 12.5%. Big numbers in a comparison question are almost always a small ratio in disguise.

Simplify the two numbers to a small ratio first. Then the difference is a count of parts and the answer is a fraction from the table.

The differenceThe numerator, always. It does not depend on how the question is phrased — only the denominator does.

The MORE/LESS inversionAsking how much MORE the larger is uses the smaller as the base. Asking how much LESS the smaller is uses the larger. More takes less; less takes more.

Ratio-firstReducing the pair to lowest terms before comparing. 1620 : 1440 becomes 9 : 8, turning a division into a table lookup.

02 Worked example

90 and 80, then 1620 and 1440

A small pair to fix the rule, then a large pair to show the shortcut. (i) 90 is what per cent more than 80? (ii) 80 is what per cent less than 90? (iii) 1620 is what per cent more than 1440?

Find the differenceThe numerator, and it is the same for both phrasings.90 − 80 = 10

Asking MORE, so take the smaller base“More than 80” measures the gap against 80.10/80 = 1/8 = 12.5% more

Asking LESS, so take the larger base“Less than 90” measures the same gap against 90 instead.10/90 = 1/9 = 11.11% less

Now the big pair — simplify it firstCancel 1620 : 1440 down before doing anything. Both divide by 180.1620 : 1440 = 9 : 8

Read the answer off the partsThe difference is one part and the question asks MORE, so the base is the smaller, 8.1/8 = 12.5% more

Parts (i) and (iii) both come to 12.5%, which is not a coincidence — 90 : 80 and 1620 : 1440 are the same ratio, 9 : 8. That is the point of simplifying: comparison questions depend only on the ratio of the two numbers, never on their size. Once the pair is in lowest terms, the answer is a unit fraction from the table.

03 The method

The rule, and the pairs worth recognising

One mechanical rule, then the ratios that generate almost every comparison question you will see.

x% more: (difference / smaller) × 100. x% less: (difference / larger) × 100. And note the “of” form is different again: larger/smaller × 100 is a percentage of, not more than.

If A is 1/n more than B, then B is 1/(n+1) less than A. So 12.5% more one way is 11.11% less the other, because 1/8 more pairs with 1/9 less. This is the same reverse pairing as the multiplier lesson, which is why the two topics are really one.

Ratio	Larger is this much MORE	Smaller is this much LESS
2 : 1	`100%`	`50%`
3 : 2	`50%`	`33.33%`
4 : 3	`33.33%`	`25%`
5 : 4	`25%`	`20%`
6 : 5	`20%`	`16.66%`
9 : 8	`12.5%`	`11.11%`
Same base for both	`wrong`	the phrasing sets the base

05 Cheat sheet

Comparison on one page

The rule, the three phrasings that are genuinely different, and the pairing.

Phrasing	Base	On 90 and 80
A is what % MORE than B	`the smaller, B`	10/80 = 12.5%
B is what % LESS than A	`the larger, A`	10/90 = 11.11%
A is what % OF B	`B, and no difference`	90/80 = 112.5%
B is what % OF A	`A, and no difference`	80/90 = 88.89%
Simplify first	`reduce the pair`	1620:1440 → 9:8
1/n more pairs with	`1/(n+1) less`	1/8 more, 1/9 less
Using one base for both	`wrong`	the phrasing decides

More takes less, less takes moreAsking how much MORE the larger is uses the smaller as the base, and vice versa. The inversion is the whole rule and it is worth saying as a phrase.

Only the ratio matters90 : 80 and 1620 : 1440 are both 9 : 8 and give identical answers. Simplify first and the arithmetic becomes a table lookup.

'Of' is a third question“90 is what per cent of 80” is 112.5% — not a difference at all. Three phrasings, three answers, one pair of numbers.

06 Where & why

Where comparison shows up

This is the single most common phrasing in quantitative aptitude, and the base choice is what is being tested nearly every time.

Data interpretation

“X% more than last year”

Almost every DI question is a comparison, and the answer options routinely include both bases so the choice is the question.

Bank PO · SSC CGL

Direct comparison questions

Usually with numbers chosen to reduce to a small ratio, which is the hint that the ratio-first habit is expected.

Profit and loss

Comparing cost with selling price

“25% profit” is exactly “the selling price is 25% more than the cost”, with the cost as the base. The same rule with a named base.

Interviews and everyday numbers

Reading a claim critically

“Prices rose 50% then fell 33%” sounds like a net rise and is exactly break-even. Knowing which base each figure uses is the skill.

When you meet a comparison, do two things before calculating: reduce the pair to lowest terms, and underline whether the question says more, less or of. Everything after that is a fraction you already know.

07 Interview questions

What gets asked

Ten, and the first three are the three genuinely different phrasings.

90 is what per cent more than 80?

12.5%. The difference is 10 and the question asks “more than 80”, so 80 is the base: 10/80 = 1/8 = 12.5%. The value after “than” is what you are comparing against.

80 is what per cent less than 90?

11.11%. The difference is still 10, but now the base is 90, giving 10/90 = 1/9 = 11.11%. Same pair of numbers, different question, different answer — and both are correct.

And 90 is what per cent of 80?

112.5%. This is a third question again: “of” means no difference is taken at all, just 90/80 × 100. Three phrasings on one pair give 12.5%, 11.11% and 112.5%, which is why reading the wording is not optional.

State the base rule.

The numerator is always the difference. The denominator is the smaller value when the question asks MORE, and the larger value when it asks LESS. More takes less; less takes more.

Why does the base invert like that?

Because you compare against whatever follows the word “than”. “A is more than B” measures A’s excess relative to B, so B is the reference. “B is less than A” measures B’s shortfall relative to A, so A is the reference.

1620 is what per cent more than 1440?

12.5%. Simplify first: 1620 : 1440 reduces to 9 : 8. The difference is one part and the question asks MORE, so the base is 8, giving 1/8 = 12.5%. Reducing the pair turns a long division into a table lookup.

Why does simplifying work at all?

Because a comparison depends only on the ratio of the two numbers, not their size. 90 : 80 and 1620 : 1440 are the same ratio and therefore give identical percentages. So reducing to lowest terms loses nothing and gains a great deal of speed.

If A is 25% more than B, by what per cent is B less than A?

20%. Twenty-five per cent more is 1/4 more, and the pairing rule says 1/n more corresponds to 1/(n+1) less — so 1/5 less, which is 20%. You can check it: if B is 4 then A is 5, and 1/5 of 5 is 1.

A salary rises 50% and then falls 33.33%. What is the net change?

Hard

A report states: “Company A’s revenue is 60% more than Company B’s.” (a) Express B’s revenue as a percentage of A’s. (b) Express B’s revenue as a percentage less than A’s. (c) A journalist rewrites the claim as “B’s revenue is 60% less than A’s.” Show that this is a materially different and much stronger claim, and quantify the discrepancy. (d) State the general relation between “x% more” and the corresponding “% less”.

Follow-up

Part (c) is why this matters outside exams. “60% more” corresponds to 37.5% less, not 60% less — the rewrite nearly doubles the apparent gap. This is a genuine and common error in published numbers, and the arithmetic to catch it is exactly this lesson.

Show the hint

Take B as 100, work out A, and then compute the shortfall as a share of A.