Aptitude · Ratio and Proportion · Model 7

2.5 and 500 are not a ratio until you look at the units

This model exists because 2.5 kg : 500 g looks like 1 : 200 and is actually 5 : 1. Nothing in the arithmetic warns you. The only defence is a habit: name both units before you write the first number down.

Convert a mismatched pair and form the ratio →

Always convert the larger unit down into the smaller one. 2.5 kg is 2500 g, so 2.5 kg : 500 g is 2500 : 500, which is 5 : 1.

01 The idea

The trap, and why nothing warns you

Find the ratio of 2.5 kg to 500 g. Write 2.5 : 500 and simplify and you get 1 : 200, which is a clean, plausible, entirely wrong answer. Convert first: 2.5 kg is 2500 g, so the ratio is 2500 : 500 = 5 : 1. The two answers are not close to each other, and no step of the wrong calculation looks suspicious.

That is what makes this model dangerous rather than difficult. Every other trap in the chapter produces something you can catch — a negative quantity, a fractional coin, a difference that does not check out. This one produces a tidy number. The only signal is in the question, in the two unit words you have to read before you start.

The rule has two halves. First, both quantities must measure the same kind of thing: you can compare a weight with a weight and a time with a time, but 10 lorries against ₹50,000 is not a ratio at all, because vehicles and money are not comparable. Second, they must be in the same unit, and if they are not, convert.

Always convert the bigger unit down. 2.5 kg becomes 2500 g rather than turning 500 g into 0.5 kg, because working in whole numbers avoids decimals in the cancelling step. There are five unit families that appear in exam papers — weight, time, distance, money and volume — and between them they account for essentially every question in this model.

Both quantities must measure the same kind of thing, in the same unit. Convert the bigger unit down into the smaller one, then form the ratio and cancel.

The unit ruleA ratio compares two quantities of the same unit. The unit cancels in the division, which is why a ratio has no unit of its own — and also why the two units have to match before you divide.

Convert downTurn the larger unit into the smaller one: 2.5 kg → 2500 g, 1 hr 15 min → 75 min, ₹12.50 → 1250 paise. Converting the other way is equally correct and brings decimals with it.

Same kind, not just same unitWeight against weight, time against time. A “ratio” of 10 lorries to ₹50,000 is not defined, because there is no conversion factor between vehicles and rupees.

02 Worked example

2.5 kg against 500 g

One pair runs the whole lesson. Find the ratio of 2.5 kg to 500 g. Watch how far the wrong answer is from the right one.

Read both units firstKilograms on the left, grams on the right. Both are weights, so a ratio exists — but not between the numbers 2.5 and 500.2.5 kg against 500 g ⇒ different units

Note what the wrong answer would beWriting the numbers down as they appear gives 2.5 : 500, which cancels to 1 : 200. There is nothing internally wrong with that arithmetic, which is exactly the problem.2.5 : 500 = 1 : 200 — wrong, and it looks fine

Convert the larger unit downOne kilogram is a thousand grams. Multiply, and now both quantities are counted in grams.2.5 × 1000 = 2500 g

Form the ratio and cancelBoth terms are in grams, so the unit cancels. Cancel the two zeros, then divide by 5.2500 : 500 = 25 : 5 = 5 : 1

Check it in chunks, with no conversion at allFive hundred grams is half a kilogram. How many halves fit into 2.5? Five. Same answer, done mentally.500 g = 0.5 kg, and 2.5 ÷ 0.5 = 5 ⇒ 5 : 1 ✓

Look at the two candidate answers: 1 : 200 and 5 : 1. They are not near neighbours, and both appear in the options of a well-set question. The chunk check in the last step is the one worth building into your habit, because it arrives at the answer by a completely different route — if the two routes disagree, you converted in the wrong direction.

03 The method

The five families, and the two rules

Five conversion factors cover essentially every question in this model. The rules either side of the table are what stop you needing to remember which one you are in.

Convert the larger unit down, then form the ratio, then cancel. 1 kg = 1000 g · 1 hour = 60 minutes · 1 km = 1000 m · ₹1 = 100 paise · 1 litre = 1000 ml. Compound units convert in stages: 1 hour 15 minutes is 60 + 15 = 75 minutes.

The chunk check catches a conversion done backwards. Ask what fraction of the larger unit the smaller quantity is, then count how many of those fit. 500 g is half a kg, and 2.5 contains five halves, so 5 : 1. 45 minutes is three quarter-hours and 75 minutes is five, so 5 : 3. 750 ml is three quarter-litres and 2.25 L is nine, so 3 : 1. It arrives by a different route, so it is a real check and not a repetition of the same arithmetic.

Question	Convert to	Ratio	Chunk check
2.5 kg : 500 g	`2500 : 500 g`	`5 : 1`	five half-kilograms
1 hr 15 min : 45 min	`75 : 45 min`	`5 : 3`	five quarter-hours against three
3.6 km : 900 m	`3600 : 900 m`	`4 : 1`	900 m is 0.9 km, and 3.6/0.9 = 4
₹12.50 : 250 paise	`1250 : 250 p`	`5 : 1`	250 p is ₹2.50, and 12.50/2.50 = 5
2.25 L : 750 ml	`2250 : 750 ml`	`3 : 1`	nine quarter-litres against three
Leaving it as 3600 : 900	`not in simplest form`	`36 : 9 is also unsimplified`	the answer is 4 : 1
10 lorries : ₹50,000	`no conversion exists`	`not a ratio`	different kinds of quantity

05 Cheat sheet

Model 7 on one page

Five factors, one direction, and the three ways this model takes marks off people who know the arithmetic perfectly well.

Case	Rule	Example
Weight	`1 kg = 1000 g`	2.5 kg : 500 g = 5 : 1
Time	`1 hr = 60 min`	1 hr 15 min : 45 min = 5 : 3
Distance	`1 km = 1000 m`	3.6 km : 900 m = 4 : 1
Money	`₹1 = 100 paise`	₹12.50 : 250 p = 5 : 1
Volume	`1 L = 1000 ml`	2.25 L : 750 ml = 3 : 1
Forgetting to convert	`gives a tidy wrong answer`	2.5 : 500 = 1 : 200
Converting but not simplifying	`right value, wrong form`	36 : 9 instead of 4 : 1

The wrong answer is always in the optionsA setter who bothers to mix units always lists the unconverted answer as a distractor. For 2.5 kg : 500 g both 1 : 200 and 5 : 1 appear, so recognising your answer in the list is no evidence at all that it is right.

Convert down, never up2.5 kg to 2500 g keeps everything whole. Turning 500 g into 0.5 kg is equally valid and leaves you cancelling decimals, which is where the arithmetic slips creep in.

Some pairs are not ratiosTwo quantities must be the same kind of thing. Lorries against rupees has no conversion factor, so there is no ratio — and a question that appears to ask for one is testing whether you say so.

06 Where & why

Where this shows up

This model is rarely a question by itself. It is a booby trap set inside a question about something else, which is why it costs whole questions rather than single marks.

TCS NQT · Wipro

“Find the ratio of 2.5 kg to 500 g”

The direct form, one mark, and the unconverted answer is always among the options. Ten seconds if you read the units, zero marks if you do not.

Time, speed and distance

km/hr against m/s

The same habit, with a two-stage factor: multiply by 1000 and divide by 3600, which is the familiar 5/18. Every speed conversion in that chapter is this model.

Time and work

Hours against days, minutes against hours

“A works 6 hours a day and B works 450 minutes a day” is a unit mismatch sitting in front of a work question. Convert before you build any ratio of efficiency.

Mixtures and profit

Litres against millilitres, quintals against kilograms

Indian papers use quintals (100 kg) and tonnes (1000 kg) freely. The conversion is the same one line, and skipping it invalidates everything downstream.

One habit finishes this model: read both unit words out loud before you write the first number. It takes two seconds and it is the only defence, because the wrong answer here never looks wrong.

07 Interview questions

What gets asked

Ten. The first two are the model; the rest are the places it hides.

Find the ratio of 2.5 kg to 500 g.

5 : 1. Convert the kilograms down: 2.5 kg is 2500 g, so the ratio is 2500 : 500 = 5 : 1. Writing 2.5 : 500 gives 1 : 200, which is wrong and which will be one of the options.

Why is 1 : 200 wrong when the arithmetic is correct?

Because the two numbers count different things. 2.5 counts kilograms and 500 counts grams, so dividing them compares nothing. A ratio is only defined between quantities in the same unit, and that is what makes the unit words part of the question.

Which direction should you convert?

Larger unit down into the smaller one. 2.5 kg → 2500 g rather than 500 g → 0.5 kg. Both are correct, but the first keeps every number whole and the second leaves you cancelling decimals.

Find the ratio of 1 hour 15 minutes to 45 minutes.

5 : 3. One hour fifteen is 75 minutes, so the ratio is 75 : 45, which cancels by 5 to 15 : 9 and then by 3 to 5 : 3. In quarter-hour chunks it is five against three, which is the same answer without any conversion.

Find the ratio of 3.6 km to 900 m.

4 : 1. Convert to 3600 : 900 and cancel. Note that 36 : 9 is the same value but is not in simplest form, and a paper will list it as a distractor precisely to catch someone who stopped one step early.

Can you write a ratio between 10 lorries and ₹50,000?

No. A ratio needs two quantities of the same kind, and there is no conversion factor between vehicles and money. You could compare 10 lorries with 20 lorries, or ₹50,000 with ₹20,000, but not one against the other.

What is the chunk check?

Work out what fraction of the larger unit the smaller quantity is, then count how many fit. 500 g is half a kilogram and 2.5 kg holds five halves, so 5 : 1. Because it reaches the answer by a different route, it genuinely catches a conversion done backwards.

Where does this model hide inside other chapters?

Speed conversions most of all — km/hr to m/s is multiply by 1000 and divide by 3600, which is the 5/18 factor. Also work questions that mix hours with minutes, and mixture questions that mix litres with millilitres. In each case the conversion is line one.

Find the ratio of 2.25 litres to 750 ml.

Hard

Tank A is filled at 2 litres per minute for 1 hour 15 minutes. Tank B is filled at 750 ml per minute for 20 minutes. (a) Find the ratio of the volumes delivered, in simplest form. (b) Find the ratio of the two filling rates and the ratio of the two times. (c) Show that the volume ratio is the compound ratio of those two, and explain in one sentence why it has to be.

Follow-up

Three separate conversions — hours to minutes, litres per minute against millilitres per minute, and millilitres back to litres — and then the compound ratio from the types-of-ratios lesson closes it. Part (c) is the reason this belongs here: volume is rate times time, so the ratio of volumes must be the product of the two ratios, and that gives you a check on all three answers at once.

Show the hint

Get both rates into litres per minute and both times into minutes before computing any volume.