📑 On this page
⚡ The short answer
The unitary method finds the value of one unit first, then multiplies up to the amount you need: 7 kg cost ₹378, so 1 kg costs ₹54 and 12 kg cost ₹648. It works only when the rate is constant. Ask whether more units mean more or less of the answer, and watch for fixed charges that break the rate.
🎬 The 30-second story
The cold-coffee aisle
1
“Five cans for ₹195. Bigger pack, bigger saving. Done.”
🛒
Aarav
Group-study night supplies.
2
“The 3-pack is ₹114. That's ₹38 a can. Yours is ₹39.”
🥫
Zoya
Zoya splits each price into one can.
3
“So the big pack is the rip-off?”
🏷️
Aarav
A 12-pack at ₹444 is ₹37 a can.
4
“We need 8 cans. At ₹38 each, that's ₹304.”
📱
Meher
Meher finds one can's price, then scales it up.
Tara's maths: Every pack was compared on the price of one can. Once you know the value of one unit, any quantity is a single multiplication away. That is the whole unitary method.
What is the unitary method, and why does it work?
Most quantities in a maths question are tied by a rate: rupees per kilo, runs per ball, kilometres per litre. The unitary method says: work out that rate first, then use it.
🧮 The formula
The unitary engine
➗
Value of one
known total ÷ known count
×
🔢
New count
how many you need
=
✅
Answer
valid while the rate stays fixed
Why does it work? A constant rate means every unit behaves the same. If 7 kg of rice cost ₹378 and no kilo is cheaper than another, each carries ₹378 ÷ 7 = ₹54, and twelve kilos are twelve copies of it. It is direct proportion in slow motion.
| Situation | The 'one unit' | Rate |
|---|---|---|
| 7 kg rice for ₹378 | 1 kg | ₹54 per kg |
| 78 runs off 52 balls | 1 ball | 1.5 runs per ball |
| ₹1,800 for a 6-hour shift | 1 hour | ₹300 per hour |
| Meal for 450 students or 270 cops | 1 student's portion | 0.6 of a cop's portion |
→ scroll to see more
📌 No constant rate, no unitary method
The method assumes each unit is worth the same. A cab with a ₹70 base fare, a bulk discount above 10 kg, or a phone that charges slower after 80% all break that. Before dividing, ask: is every unit really identical?
How do you solve a unitary method question step by step?
- 1
Find the value of oneName the unit (one kg, one ball, one hour), then divide the known total by the known count.
- 2
Check the directionMore units should mean more of the answer (direct) or less (inverse). Decide before you multiply.
- 3
Scale and sanity-checkMultiply by the new count, then ask if the size of the answer makes sense.
✍️ Worked example
Warm-up
⏱ 20 sec
Kabir's rice sack
Kabir sells 7 kg of rice for ₹378. At the same rate, what do 12 kg cost?
- 1Unit: 1 kg. Value of one = 378 ÷ 7 = ₹54.
- 2More rice, more money: direct, so multiply.
- 312 × 54 = 648. Sanity check: 12 kg is a bit under double 7 kg, and ₹648 is a bit under double ₹378.
Answer: ₹648
⚡ The exam-hall shortcut
Write it as one line: 378 × 12/7. Cancel 378 ÷ 7 = 54 first, then 54 × 12 = 648.
✍️ Worked example
CLAT level
⏱ 30 sec
The strike-rate question
Rohan's favourite opener scored 78 runs off 52 balls. If he keeps the same scoring rate, how many runs will he make in the next 5 overs (30 balls)? What is his strike rate?
- 1Unit: 1 ball. Runs per ball = 78 ÷ 52 = 1.5.
- 2Overs into balls first: 5 overs = 30 balls. Mixed units are the hidden step.
- 3Runs = 30 × 1.5 = 45.
- 4Strike rate is runs per 100 balls: 1.5 × 100 = 150.
Answer: 45 runs; strike rate 150
⚡ Use a convenient unit
78 and 52 are both multiples of 26: 3 runs every 2 balls. 30 balls is 15 pairs, so 45 runs.
What if more units means less? Unitary method for inverse proportion
Sometimes the 'one' takes longer, not less. If 6 printers finish a job in 5 hours, one printer alone needs 6 times as long. So for inverse questions the first step is a multiplication, not a division. Think of it as finding the total job size, then sharing it out.
✍️ Worked example
CLAT level
⏱ 30 sec
Two printers down
Six identical printers print the fest magazine in 5 hours. On the day, two of them jam and are switched off. How long will the remaining printers take?
- 1Fewer printers, more time: inverse.
- 2One printer alone: 6 × 5 = 30 printer-hours. That is the size of the job.
- 34 printers share it: 30 ÷ 4 = 7.5 hours.
Answer: 7 hours 30 minutes
⚡ The exam-hall shortcut
5 × 6/4 = 7.5. Fewer printers, so multiply by the fraction bigger than 1.
What is the fastest way to use the unitary method in the exam?
You do not always need the value of exactly one. Pick the most convenient unit. In 2019's mess question, 450 students and 270 cops eat the same meal; both numbers are 90 × something, so the convenient unit is a block of 90: 5 students eat what 3 cops eat. And when you compare deals, you do not even need the unit price: cross-multiply.
📊 The data
Price of one can, pack by pack
3-pack, ₹114 · Zoya's pick
₹38
5-pack, ₹195 · Aarav's pick
₹39
12-pack, ₹444
₹37
The 5-pack is the worst deal per can. Cross-multiply check: 114 × 5 = 570 and 195 × 3 = 585, so the 3-pack is cheaper per can. The 12-pack is cheapest per can, but only if you need 12.
💡 Multiply first, divide last
Write the whole calculation as one fraction (378 × 12/7) and cancel before you multiply. Rounding the per-unit value early, say ₹38.57 for 270/7, is how a correct method lands on a wrong option.
🎛️ Try it yourself — change any number
Try it: what do 8 cans cost?
Per unit
38
Answer
304
114 ÷ 3 × 8 = 304
The 3-pack gives ₹38 a can and ₹304 for 8. Now put in the 5-pack (5 cans, ₹195): ₹39 a can, ₹312 for 8. Then try 12 cans for ₹444.
How does the unitary method hide inside a CLAT caselet?
CLAT never says 'use the unitary method'. It gives rates in different shapes (a shift fee, a per-order rate, a package price) and asks you to compare them. Bring every rate to the same unit first. Take this mini caselet:
For the college fest, stall assistants are paid ₹1,800 for a 6-hour shift. Delivery runners get ₹42 an order and manage 5 orders an hour. Photographers charge ₹4,500 for a 10-hour package. Sound technicians get ₹2,640 for an 8-hour day.
📊 The data
Every role, brought to rupees per hour
Stall assistant · 1,800 ÷ 6
₹300
Delivery runner · 42 × 5
₹210
Photographer · 4,500 ÷ 10
₹450
Sound tech · 2,640 ÷ 8
₹330
Four shapes of pay, one unit.
- ✓Who earns the most per hour? The photographer, at ₹450.
- ✓What does a runner earn in a 7-hour day? 210 × 7 = ₹1,470 (or 35 orders × ₹42).
- ✓How many hours must a stall assistant work to earn one photographer package? 4,500 ÷ 300 = 15 hours.
- ✓What is the total paid to stall assistants? Cannot be determined: the caselet never says how many there are. A rate without a count gives no total.
What traps does CLAT set in unitary method questions?
⚠️ The fixed charge breaks the rate
If 10 km costs ₹230 and 20 km costs ₹390, a kilometre is not ₹23. The extra 10 km cost ₹160, so the rate is ₹16 a km on top of a fixed amount.
✍️ Worked example
Tricky
⏱ 45 sec
The cab-fare trap
An app cab charged Aarav ₹230 for a 10 km ride and ₹390 for a 20 km ride. Same pricing, no surge. What will a 35 km ride cost?
- 1Test the rate: if the fare were purely per km, 20 km would cost 2 × 230 = ₹460. It costs ₹390, so there is a fixed part.
- 2Per-km rate from the difference: (390 − 230) ÷ (20 − 10) = ₹16 per km.
- 3Fixed part: 230 − 10 × 16 = ₹70.
- 435 km: 70 + 35 × 16 = 70 + 560 = ₹630.
Answer: ₹630 (not ₹805, which is the naive 23 × 35)
⚡ The exam-hall shortcut
Apply the unitary method to the change, not the totals: each extra km is ₹16. From 20 km to 35 km is 15 more km: 390 + 15 × 16 = 630.
- The used-up base. 'If 300 students have already eaten': scale only what is left, not the whole stock.
- Wrong direction. More printers giving more hours is a red flag.
- Mixed units. Overs and balls, ml and litres, hours and minutes, dozens and pieces. Convert before you divide.
- % more read as rupees. '48% more than ₹200' is ₹296, not ₹248.
How has CLAT asked the unitary method?
📝 Asked in CLAT 2019
· Q53
Unitary method, equal meal
Stand-alone question (no passage).
A mess contractor can either serve 450 students with the meal that he prepares or can cater to 270 cops with the same meal. If 300 students have already eaten in the mess, how many cops can be fed with the remaining meal?
A20
B45
C90
D180
Reveal answer + reasoning
Answer: C
Our solution (2019 has no official key). Unit: the meal of one student. The whole meal = 450 student-portions = 270 cop-portions, so one student-portion = 270/450 = 0.6 of a cop-portion. After 300 students eat, 150 student-portions are left: 150 × 0.6 = 90 cops. Convenient unit: 450 : 270 = 5 : 3, so 150 students' food feeds 150 × 3/5 = 90 cops. Time: about 30 seconds.
Why the others fail
- A — Not reachable by any consistent route; a filler option.
- B — Half of 90: a halving step that the question never asks for.
- D — 180 = 300 × 0.6, the cops' worth of the food already eaten. Right method, wrong base.
📝 Asked in CLAT 2025
· Q112
Rate from '% more'
…Men earn more than women across all forms of work, the gap greatest for the self-employed. In 2023, male self-employed workers earned 2.8 times that of women. In contrast, male regular wage workers earned 24% more than women and male casual workers earned 48% more. The gender gap in earnings is still a persistent phenomenon…
If a female casual worker earns Rs. 200 per hour, what is the hourly wage of a male casual worker, given that male casual workers earn 48% more than female casual workers?
ARs. 480
BRs. 296
CRs. 248
DCannot be determined
Reveal answer + reasoning
Answer: B
Treat the woman's wage as the unit. '48% more' means for every ₹1 she earns, a man earns ₹1.48. Her wage is ₹200 an hour, so his is 200 × 1.48 = ₹296. Check: 48% of 200 is 96, and 200 + 96 = 296. Time: about 15 seconds. The passage's other figures are noise here.
Why the others fail
- A — 480 is 2.4 times her wage: a scaling slip, nowhere near 48% more.
- C — 248 adds ₹48 instead of 48% of ₹200. The percentage needs a base.
- D — The question gives both her hourly wage and the 48% gap, which is all you need. 'Cannot be determined' is a trap here, not a safe exit.
💥 Myth vs fact
Unitary method myths that cost marks
🙅 Myth
You must always find the value of exactly one.
Tap to bust it →
✅ Fact
Any convenient unit works. '5 students eat what 3 cops eat' is faster than 0.6 of a portion.
🙅 Myth
The bigger pack is always cheaper.
Tap to bust it →
✅ Fact
Only the price per unit tells you. ₹195 for 5 is worse than ₹114 for 3.
🙅 Myth
If 2 hours cost ₹650, 4 hours cost ₹1,300.
Tap to bust it →
✅ Fact
Only if there is no fixed charge. Check whether two data points actually double together.
Quick check: can you find the unit?
🎯 Quick quiz
Five questions, three minutes
0 / 5
Q1. 14 metres of fabric cost ₹840. What do 9 metres cost?
One metre = 840 ÷ 14 = ₹60, so 9 metres = 9 × 60 = ₹540.A hostel's water tank supplies 25 rooms for 12 days. During the holidays, 5 rooms are locked and use no water.
Q2. How many days will a full tank now last?
Inverse. One room alone: 25 × 12 = 300 room-days. 20 rooms share it: 300 ÷ 20 = 15 days. 9.6 multiplies the wrong way.Q3. Which pack of coffee powder is the best value?
Price per 100 g: ₹24.80, ₹24, ₹23, ₹23.60. The 750 g pack wins, and it is not the biggest.Q4. A train covers 228 km in 3 hours. At the same speed, how far does it go in 4 hours 30 minutes?
Speed = 228 ÷ 3 = 76 km/h. 4 h 30 min = 4.5 h, so 76 × 4.5 = 342 km. 304 km uses only 4 hours.A plumber charged ₹650 for a 2-hour job and ₹1,050 for a 4-hour job, with the same pricing.
Q5. What will he charge for a 5-hour job?
2 extra hours cost ₹400, so ₹200 an hour plus a fixed ₹250 (650 − 400). 5 hours = 250 + 1,000 = ₹1,250. ₹1,625 and ₹1,312.50 ignore the fixed charge.🎯 The unitary method in a nutshell
- Find the value of one unit, then multiply by the count you need.
- It works only when the rate is constant: no fixed charge, no bulk discount.
- Direct: divide to get one, multiply to scale. Inverse: multiply to get the total job, divide to share it.
- Any convenient unit works; it need not be one.
- In caselets, bring every rate to the same unit before comparing.
📎 Formula card
- Direct: answer = (total ÷ count) × new count = total × new count/old count
- Inverse: new time = (workers × time) ÷ new workers
- Fixed charge: rate = (C₂ − C₁) ÷ (Q₂ − Q₁); fixed part = C₁ − rate × Q₁
- Compare deals: P₁/Q₁ vs P₂/Q₂ → compare P₁ × Q₂ with P₂ × Q₁
- % more: x% more than A = A × (100 + x)/100; strike rate = runs ÷ balls × 100
Frequently asked questions
What is the unitary method in maths?
The unitary method finds the value of one unit first and then multiplies to get the value of any number of units. If 7 kg of rice cost ₹378, one kilo costs ₹54, so 12 kilos cost ₹648. It works whenever each unit is worth the same, that is, whenever the rate is constant.
What is the difference between the unitary method and proportion?
They give the same answer. Proportion sets up an equation such as 7/378 = 12/x and solves it in one line. The unitary method breaks it into two visible steps: find the value of one, then scale. The unitary method is slower but harder to get wrong.
How do you use the unitary method for inverse proportion?
Find the total job first by multiplying, then divide by the new number. If 6 printers take 5 hours, one printer needs 6 × 5 = 30 hours, so 4 printers need 30 ÷ 4 = 7.5 hours. One printer takes longer, so step one is a multiplication.
How do you find which pack is the better deal?
Compare the price of one unit in each pack. A 3-pack for ₹114 is ₹38 a can and a 5-pack for ₹195 is ₹39 a can, so the smaller pack is cheaper per can. Or cross-multiply: 114 × 5 = 570 is less than 195 × 3 = 585.
Is the unitary method asked in CLAT?
Yes, though rarely by name. CLAT 2019 asked a mess-meal question that is pure unitary method, and CLAT 2025 asked for a male worker's hourly wage from a '48% more' figure. In caselets it appears whenever rates must be brought to the same unit before comparing.
Keep going
← Previous topic
Direct and Inverse Proportion
Fixed ratio or fixed product? The one test that solves both
Next topic →
Partnership: Sharing Profit by Capital × Time
Profit follows capital × time: split any business profit in 30 sec
📚
Part of the chapter
Ratio & Proportion for CLAT Quantitative Techniques
See how this topic fits the whole of Ratio & Proportion →
Connected topics in other chapters
Direct and Inverse Proportion
The fixed-ratio and fixed-product ideas behind every unitary step, solved the one-line way.
Cost, Revenue and Per-Unit Price
Per-unit price is the unitary method in a business caselet: cost per item, revenue per sale.
Time and Work: the LCM Method
One worker's one-day work is the unitary idea taken to full CLAT questions.
Speed, Distance and Time
Speed is just distance per one hour. The same scaling, with units to watch.
Percentage Change
'48% more' turns into a multiplier of 1.48: the bridge between rates and percentages.
Every topic in Ratio & Proportion
- 1.Ratio Basics: Simplifying and Comparing Ratios
- 2.Dividing a Quantity in a Given Ratio
- 3.Combining Ratios: A:B, B:C and Overall Ratios
- 4.Proportion, Third and Mean Proportional
- 5.Direct and Inverse Proportion
- 6.The Unitary Method (you're here)
- 7.Partnership: Sharing Profit by Capital × Time
- 8.Problems on Ages: The Constant-Gap Trick