Aptitude · Ratio and Proportion · Fundamentals
Multiply both terms freely. Never add to them.
A ratio compares two quantities of the same kind. You can scale both terms by any number you like and the comparison survives, which is why 18 : 12 and 3 : 2 say the same thing. Add to both terms and it does not survive — and that one asymmetry generates half the questions in this chapter.
Simplify a pair, then compare it with another →01 The idea
What a ratio actually says
A class has 18 boys and 12 girls. You can report that as “six more boys than girls”, or you can report the ratio: 18 : 12, which cuts down to 3 : 2. The difference matters. The first statement is destroyed if the class doubles in size; the ratio is not. A ratio is a statement about relative size, and relative size is what survives scaling.
The one condition is that both quantities are measured in the same unit. 10 lorries against ₹50,000 is not a ratio, because vehicles and money are not the same kind of thing. Worse, 2 kg against 500 g looks like a ratio and is not one either — you have to convert first, to 2000 g : 500 g, which is 4 : 1. An entire exam model exists to punish people who skip that conversion.
Order is part of the statement. 3 : 2 and 2 : 3 are different ratios, and the sentence in the question fixes which one you want. The first term has a name — the antecedent — and the second is the consequent. When a question says “the ratio of boys to girls”, boys go first, and the marks for the whole question turn on that.
The last thing to fix now, because it causes more lost marks than anything else in the chapter: 3 : 2 does not mean boys are 3/2 of the class. It means that for every 3 boys there are 2 girls, so the class comes in blocks of 5. Boys are 3/5 of the class — 60%. A ratio compares the parts with each other; a fraction compares one part with the whole.
02 Worked example
18 boys and 12 girls, worked all the way down
One class runs this whole lesson. A class has 18 boys and 12 girls. Write the ratio of boys to girls in simplest form, state what fraction of the class is boys, and say whether this class is more boy-heavy than a class with a 7 : 5 ratio.
Read that third step again, because Model 4 in this module exists entirely because of it. Adding a constant to both terms genuinely changes a ratio, and the size of that change carries information — if you know the ratio before and after, you can work backwards to the actual numbers. A rule that only ever said “you cannot do that” would be worth one line; this one is worth a whole model.
03 The method
The three operations, and which of them is safe
Everything you will ever do to a ratio is one of three moves. Two are safe and one is not, and knowing which is which is most of the chapter.
| Move on 18 : 12 | Result | Safe? |
|---|---|---|
| Divide both by 6 | 3 : 2 | Yes — this is simplifying |
| Multiply both by 4 | 72 : 48 = 3 : 2 | Yes |
| Add 2 to both | 20 : 14 = 10 : 7 | Changes it — sometimes on purpose |
| Add 2 to the first only | 20 : 12 = 5 : 3 | Changes it — sometimes on purpose |
| Swap the terms | 12 : 18 = 2 : 3 | A different ratio, not the same one |
| Divide the first by 6 only | 3 : 12 = 1 : 4 | Never — both terms or neither |
| Compare with 7 : 5 | 3×5 = 15 > 2×7 = 14 | 3 : 2 is the larger |
05 Cheat sheet
Ratio basics on one page
The moves, the traps and the two conversions between a ratio and a percentage that get asked directly.
| Case | Rule | On 18 : 12 |
|---|---|---|
| Simplify | divide both by the HCF | ÷6 → 3 : 2 |
| Scale up | multiply both by k | ×4 → 72 : 48 = 3 : 2 |
| Share of the total | a/(a+b) | 3/5 = 60% boys |
| Compare two ratios | ad vs bc | 3×5 = 15 > 2×7 = 14 |
| Ratio as a percentage gap | (a−b)/b × 100 | 3 : 2 → 50% more boys |
| Adding k to both terms | changes the ratio | +2 → 10 : 7 |
| Different units | convert before comparing | 2 kg : 500 g is 4 : 1, not 1 : 250 |
06 Where & why
Where this shows up
Ratio fundamentals are rarely a whole question on their own. They are the first line of a question about something else, which is why an error here is expensive.
One or two marks, usually with a unit conversion buried in it. The conversion is the question; the simplification is bookkeeping.
“A is 25% more than B, find A : B” and its reverse. Both directions are one line once you set the base to 100.
Models 2 to 9 all start by getting a clean integer ratio. A wrong simplification propagates through the entire solution with no warning.
A pie chart is a ratio drawn as angles. Reading a 3 : 2 split as 60% against 40% is exactly the ratio-to-share step in this lesson.
07 Interview questions
What gets asked
Ten, in the order an interviewer escalates — definition, the rule, the traps, then the honest question about when any of this matters.
What is a ratio?
What can you do to a ratio without changing it?
Why does adding to both terms change the ratio?
Is 3 : 2 the same as the fraction 3/2?
Find the ratio of 2 kg to 500 g.
Which is larger, 3 : 2 or 7 : 5?
A : B = 3 : 2. By what percentage is A more than B?
Ratio or percentage — when would you use each?
Does a ratio have units?
When would you actually reach for a ratio rather than the raw numbers?
08 Practice problems
Six on the basics
Do the first two in your head. The unit conversions in the middle two are where marks are actually lost, so write those out.