If one topic quietly powers CLAT Quantitative Techniques, it is ratio and proportion. The Quant section is data-interpretation: a short passage, table or chart, then a set of questions. Most are really asking one thing — how does this quantity compare to that one, and how do I split the total? That is ratio. Master it and a Quant passage turns into reliable marks in a section that is only Class-10 maths.
📌 Why ratio matters more than it looks
CLAT Quant is roughly 10% of the paper, and almost every set leans on ratio: dividing a budget, comparing the share of two products, finding what percentage one slice is of the whole. You do not need advanced maths — you need to handle ratios cleanly and quickly.
What a ratio actually is
A ratio compares two quantities of the same kind by division. Writing a : b says 'for every a units of the first, there are b units of the second'. A class with 18 boys and 12 girls has a boys-to-girls ratio of 18 : 12. The two numbers are the terms of the ratio; their order carries meaning, so 18 : 12 is not the same statement as 12 : 18.
- ✓Same units — a ratio compares like with like. Convert first: 2 km to 500 m is 2000 : 500, i.e. 4 : 1, not 2 : 500.
- ✓No units in the answer — a ratio is a pure number. The metres cancel; what is left is just '4 to 1'.
- ✓Order matters — the first term names the first quantity. 'Boys to girls 3 : 2' and 'girls to boys 3 : 2' are different.
- ✓It is a comparison, not a count — 18 : 12 and 3 : 2 describe the same class. A ratio gives the proportion, never the headcount on its own.
Simplifying a ratio
A ratio is in its simplest form when its terms share no common factor other than 1 — exactly like a fraction in lowest terms. Divide both terms by their highest common factor. For 18 : 12, the HCF is 6, so it simplifies to 3 : 2.
- 1
Match the unitsConvert both quantities to the same unit before you write the ratio — rupees with rupees, minutes with minutes.
- 2
Write the two termsPut them in the order the question names, first quantity first. Clear any fractions by multiplying through.
- 3
Divide by the HCFFind the highest common factor of the two terms and divide both by it: 18 : 12 → divide by 6 → 3 : 2.
💡 Treat a ratio like a fraction
Anything you may do to a fraction, you may do to a ratio: multiply or divide both terms by the same number and the ratio is unchanged. 3 : 2 = 6 : 4 = 30 : 20. This single fact is the engine behind comparing ratios and scaling quantities up or down.
Dividing a quantity in a given ratio — the parts method
This is the most useful single skill in the chapter. To split a total in a ratio, count the parts. In a ratio a : b, the total is a + b parts; one part is the total divided by that sum; each share is its number of parts times the value of one part.
- 1
Add the ratio termsFor a : b, the total number of equal parts is a + b. Splitting ₹4,500 in 5 : 4 gives 5 + 4 = 9 parts.
- 2
Find the value of one partDivide the total quantity by the number of parts. ₹4,500 ÷ 9 = ₹500 per part.
- 3
Multiply out each shareFirst share = 5 × ₹500 = ₹2,500. Second share = 4 × ₹500 = ₹2,000. They add back to ₹4,500 — always check this.
⚠️ A ratio is NOT the actual quantity — and the order is fixed
The most punished mistake in CLAT Quant: treating the ratio number as the real figure. A 3 : 2 split of 200 sweets is not 3 and 2 sweets — it is 120 and 80. Always convert ratio → parts → real value before answering. And keep the order straight: if the passage says 'urban to rural is 7 : 5', the 7 belongs to urban. Swap the terms and every later answer flips. Read the order off the question, never assume it.
🧩 Worked example
A district sanctions a road-safety fund of Rs 1,80,000, to be divided among three towns, Aroli, Bansa and Chitwan, in the ratio 4 : 3 : 2 in proportion to the length of road in each town. The whole fund is allocated with nothing held back.
How much money does Bansa receive from the fund?
ARs 40,000
BRs 60,000
CRs 80,000
DRs 90,000
▸ Show solution
Answer: B. Use the parts method. Total parts = 4 + 3 + 2 = 9. Value of one part = ₹1,80,000 ÷ 9 = ₹20,000. Bansa's share = 3 parts = 3 × ₹20,000 = ₹60,000. (Check: Aroli ₹80,000 + Bansa ₹60,000 + Chitwan ₹40,000 = ₹1,80,000.) The answer is B. Note that ₹40,000 (A) is Chitwan's share — a classic wrong-order trap.
Combining and comparing ratios
CLAT loves asking which of two categories is larger, or chaining ratios together. Two clean techniques cover almost every case: cross-multiply to compare, and make a common middle term to combine.
- Comparing two ratios — to test whether 3 : 4 is bigger or smaller than 5 : 7, treat them as fractions 3/4 and 5/7 and cross-multiply: 3 × 7 = 21 versus 5 × 4 = 20. Since 21 > 20, 3 : 4 > 5 : 7.
- Combining ratios (the bridge term) — if A : B = 2 : 3 and B : C = 4 : 5, scale them so B matches. Make B = 12 in both: A : B = 8 : 12 and B : C = 12 : 15, giving A : B : C = 8 : 12 : 15.
- Equivalent ratios — 2 : 3, 4 : 6 and 20 : 30 are all equal. Spotting this lets you scale a ratio to convenient numbers for a chart total.
ℹ️ Cross-multiplication, cleanly
To compare a : b with c : d, ask whether a × d is more than, less than or equal to b × c. Bigger product on the left means the left ratio is larger. This is the same move you will use for proportion in a moment — it is one rule doing two jobs.
Proportion: when two ratios are equal
A proportion states that two ratios are equal: a : b :: c : d, read 'a is to b as c is to d', meaning a/b = c/d. The outer terms a and d are the extremes; the inner terms b and c are the means.
In any proportion, the product of the extremes equals the product of the means.
That single rule solves almost every proportion question. If three terms are known, cross-multiply and divide for the fourth. For 3 : 8 :: 9 : x, the rule gives 3x = 72, so x = 24.
Mean proportional
When the two means are the same number — a : b :: b : c — that middle value b is called the mean proportional between a and c. By the cross rule, b × b = a × c, so b is the square root of (a × c). The mean proportional between 4 and 9 is √(4 × 9) = √36 = 6.
💡 Spot the mean proportional in one line
If a question asks for 'the mean proportional between two numbers', multiply them and take the square root — that is the whole method. Between 8 and 18: √(8 × 18) = √144 = 12. No equations needed.
🧩 Worked example
A printing machine produces pages at a steady rate. The operator records that the machine prints 240 pages in 18 minutes during a test run, and that the rate stays constant throughout the day.
At the same rate, how many minutes will the machine take to print 400 pages?
A24 minutes
B27 minutes
C30 minutes
D32 minutes
▸ Show solution
Answer: C. Pages and time are in direct proportion at a steady rate, so set up the proportion 240 : 18 :: 400 : x. By the cross rule, 240 × x = 18 × 400 = 7200, so x = 7200 ÷ 240 = 30 minutes. (Quick check by unitary method: 18 ÷ 240 = 0.075 min per page; 0.075 × 400 = 30.) The answer is C.
Direct vs inverse proportion
Two quantities can be linked in opposite ways, and reading which one a question intends is the make-or-break step. In direct proportion they rise and fall together; in inverse proportion one rises as the other falls.
| Direct proportion | Inverse proportion | |
|---|---|---|
| What happens | Both increase together / both decrease together | One increases as the other decreases |
| The rule | a/b stays constant — ratio is fixed | a × b stays constant — product is fixed |
| Everyday example | More items bought → more total cost | More workers on a job → fewer days to finish |
| Set-up | x1/y1 = x2/y2 (cross-multiply) | x1 × y1 = x2 × y2 |
| Quick test | Double the cause → double the effect | Double the cause → halve the effect |
📌 The two-second decision
Before solving, ask: 'if the first quantity goes up, does the second go up or down?' Up together → direct (keep the ratio constant). One up while the other goes down → inverse (keep the product constant). Speed → time for a fixed distance is inverse; men → days for a fixed job is inverse; quantity → cost is direct.
🧩 Worked example
A relief camp has enough food for 60 people to last 24 days, with everyone eating the same daily amount. Just as the camp opens, the organisers learn that 90 people will actually be staying, not 60. No extra food can be brought in.
For how many days will the food now last?
A12 days
B16 days
C18 days
D20 days
▸ Show solution
Answer: B. More people eating the same store means the food lasts fewer days — this is inverse proportion, so people × days is constant. 60 × 24 = 1440. With 90 people: 90 × days = 1440, so days = 1440 ÷ 90 = 16 days. The answer is B. The trap is to treat it as direct and get a larger number; always ask which way the second quantity moves.
The unitary method
The unitary method is the plain-English cousin of proportion: find the value of one unit first, then scale up. It is slower to write but almost impossible to get wrong — a safe fallback under exam pressure.
- 1
Find the value of one unitDivide the known quantity by the known count. If 6 notebooks cost ₹150, one costs ₹150 ÷ 6 = ₹25.
- 2
Scale to the number you wantMultiply the value of one unit by the new count: 10 notebooks cost ₹25 × 10 = ₹250.
- 3
Mind the direction for inverse casesFor inverse problems (men and days), find total 'work' first — 8 men × 15 days = 120 man-days — then divide by the new count of men.
💡 Use the unitary method to sanity-check
Even when you solve by proportion, a quick unitary check catches careless errors. Found that 400 pages take 30 minutes? One page = 18/240 = 0.075 min, and 0.075 × 400 = 30. The two methods agreeing is your confidence that the answer is right.
Drill ratio & proportion now
10 drills, 150 questions — real CLAT-style data passages with four close options and full working in every answer.
Ratio in data interpretation
Here is where the chapter pays off. CLAT Quant gives a passage, table or pie chart and asks you to split a total among categories, compare two slices, or find what percentage one part is of the whole. Every one of these is a ratio dressed in a story.
- ✓Splitting a total — a budget or population given as a total, divided among categories in a stated ratio. Use the parts method.
- ✓Comparing categories — 'how many more X than Y?' or 'X is how many times Y?'. Read both figures off the chart, then form the ratio.
- ✓Part of a whole — 'what percentage of the total is X?'. That is X : total, turned into a percentage by multiplying by 100.
- ✓Pie charts as ratios — each slice's angle out of 360°, or its percentage out of 100, is a ratio you scale up to the real total given in the passage.
ℹ️ On a pie chart, the angle IS a ratio
A pie slice of 90° is 90/360 = 1/4 of the whole. If the chart's total is ₹40,000, that slice is ₹40,000 × (90/360) = ₹10,000. Whether the chart labels slices in degrees or in percentages, treat the slice as a ratio of the whole and scale to the real total in the passage.
🧩 Worked example
A school's annual budget of Rs 12,00,000 is shown on a pie chart with four heads: Salaries, Infrastructure, Activities and Reserve. The chart shows Salaries taking up half of the circle, Infrastructure a quarter, Activities one-sixth, and the Reserve the remaining slice.
How much more is spent on Salaries than on Infrastructure?
ARs 2,00,000
BRs 3,00,000
CRs 4,00,000
DRs 6,00,000
▸ Show solution
Answer: B. Salaries = half = ₹12,00,000 × 1/2 = ₹6,00,000. Infrastructure = a quarter = ₹12,00,000 × 1/4 = ₹3,00,000. The difference = ₹6,00,000 − ₹3,00,000 = ₹3,00,000. The answer is B. The trap option ₹6,00,000 (D) is the Salaries figure itself — the question asks for the difference, not the larger slice.
🧩 Worked example
A car dealership sold 360 vehicles last quarter. A table breaks the sales into three types in the ratio Hatchbacks : Sedans : SUVs = 5 : 4 : 3. The manager wants to know each type's share of total sales as a percentage.
What percentage of the vehicles sold were SUVs?
A20%
B25%
C30%
D33%
▸ Show solution
Answer: B. Total parts = 5 + 4 + 3 = 12. SUVs are 3 parts, so the SUV share is 3/12 = 1/4. As a percentage, 1/4 × 100 = 25%. (You can confirm with counts: one part = 360 ÷ 12 = 30 vehicles, so SUVs = 3 × 30 = 90, and 90/360 = 25%.) The answer is B. Note you never needed the 360 to get the percentage — the ratio alone gives the share.
Partnership: share of profit as a ratio
A neat real-world use of ratio CLAT sometimes wraps into a passage is partnership. When partners invest different amounts, they share the profit in the ratio of what they put in — or, where investments run for different times, in the ratio of investment × time. It is the parts method applied to money.
- Equal time — partners A and B invest ₹30,000 and ₹20,000 for the same period; profit is shared 30,000 : 20,000 = 3 : 2.
- Different time — multiply each investment by the months it stayed in. ₹10,000 for 12 months versus ₹15,000 for 8 months gives 1,20,000 : 1,20,000 = 1 : 1, an equal split despite unequal sums.
- Then split the profit — once you have the ratio, share the total profit by the parts method, exactly as with any other quantity.
📌 Partnership is just 'divide in a ratio'
Do not memorise a separate formula. Build the investment ratio (using investment × time if periods differ), then divide the profit in that ratio with the parts method. One technique, many disguises — which is the theme of this whole chapter.
🎯 Ratio & proportion in a nutshell
- A ratio a : b compares like quantities by division. Same units, order matters, simplify by dividing both terms by their HCF.
- To divide a total, add the terms to get the parts, find the value of one part, then multiply out each share — and check they sum back.
- A proportion a : b :: c : d means a/b = c/d; cross-multiply so that product of extremes = product of means.
- The mean proportional between two numbers is the square root of their product.
- Direct proportion keeps the ratio constant (both move together); inverse keeps the product constant (one up, one down).
- In data interpretation, splitting a total, comparing slices and finding a part-of-whole percentage are all ratio. A ratio is never the actual quantity — convert to parts and real values, and keep the order fixed.
Common mistakes to stop making
- ✓Reporting the ratio number as the answer — saying '3 sweets' when the 3 : 2 split of 200 means 120. Always go ratio → parts → real value.
- ✓Swapping the order of terms — giving the urban figure when the question's order made the answer rural. Read the order off the passage every time.
- ✓Choosing direct when it is inverse — more men should mean fewer days; if your answer grew when it should shrink, you used the wrong relationship.
- ✓Forgetting to match units before forming a ratio — 2 km and 500 m become 2000 m : 500 m = 4 : 1, not 2 : 500.
- ✓Answering a different question than asked — giving a single share when asked for the difference, or a count when asked for a percentage.
🧮
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Section guide
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Frequently asked questions
Is ratio and proportion important for CLAT Quantitative Techniques?
Very. Quant is about 10% of the CLAT paper and is data-interpretation in style — passages, tables and charts. Most questions reduce to a ratio: splitting a total, comparing two categories, or finding what percentage one part is of the whole. Get comfortable with ratios and you unlock the bulk of the Quant marks, which is only Class-10 maths.
How do I divide a quantity in a given ratio?
Use the parts method. Add the ratio terms to get the total number of equal parts, divide the total quantity by that number to find the value of one part, then multiply each ratio term by the value of one part. Splitting ₹4,500 in 5 : 4 gives 9 parts, ₹500 per part, so the shares are ₹2,500 and ₹2,000. Always check they add back to the total.
What is the difference between direct and inverse proportion?
In direct proportion two quantities rise and fall together, so their ratio stays constant — more items bought means more total cost. In inverse proportion one rises as the other falls, so their product stays constant — more workers on a job means fewer days to finish. Before solving, ask whether the second quantity goes up or down when the first goes up, and pick accordingly.
What does a : b :: c : d mean and how do I solve it?
It is a proportion, read 'a is to b as c is to d', meaning the ratios are equal: a/b = c/d. Solve it with the cross rule — the product of the extremes (a and d) equals the product of the means (b and c). If three terms are known, cross-multiply and divide for the fourth. For 3 : 8 :: 9 : x, 3x = 72, so x = 24.
How is ratio used in data-interpretation questions?
Directly. To split a total across categories you use the parts method; to compare two slices you read both figures and form their ratio; to find a part of the whole you express it as a percentage. On a pie chart, each slice's angle out of 360° or percentage out of 100 is a ratio you scale up to the real total given in the passage.
What is the mean proportional between two numbers?
When a proportion has the form a : b :: b : c, the repeated middle term b is the mean proportional between a and c. By the cross rule b × b = a × c, so b is the square root of the product a × c. The mean proportional between 4 and 9 is the square root of 36, which is 6. Multiply the two numbers and take the square root — that is the whole method.
What is the most common ratio mistake in CLAT Quant?
Treating the ratio number as the actual quantity. A 3 : 2 split of 200 is not 3 and 2 but 120 and 80, so you must convert ratio to parts to real values. The second most common error is swapping the order of terms — if the passage says urban to rural is 7 : 5, the 7 belongs to urban. Read the order off the question every time.