CLAT Quantitative Techniques
The CLAT quant formula sheet
One page, every formula, worked
CLAT quant is Class 10 arithmetic on data: 10–14 questions built on passages and tables. These are the formulas those questions lean on, each with an example worked out, and two data sets solved step by step.
Updated
Fractions you should know as percentages
Most CLAT divisions are one of these in disguise: 54 out of 180 is 3/10, so 30%.
Percentages
x% of y
x/100 × y
What is 18% of 450?
18/100 × 450 = 81
Percentage change
(new − old) ÷ old × 100
A price rises from ₹250 to ₹290. By what percentage?
(290 − 250) ÷ 250 × 100 = 16%
Two changes in a row (a%, then b%)
a + b + ab/100 (use minus signs for falls)
A value rises 20% and then falls 10%. What is the net change?
20 + (−10) + (20 × −10)/100 = 8%, a net rise
Percentage points vs per cent
points = new% − old%; per cent = points ÷ old% × 100
A pass rate goes from 40% to 50%. By how many per cent did it rise?
It rose 10 percentage points, which is (10 ÷ 40) × 100 = 25%
If A is r% more than B, B is less than A by
r ÷ (100 + r) × 100 %
A earns 25% more than B. By what percentage is B's pay less than A's?
25 ÷ 125 × 100 = 20%
Ratio and proportion
Divide N in the ratio a : b
a/(a+b) × N and b/(a+b) × N
Split ₹1,200 in the ratio 3 : 5. What is the larger share?
5/8 × 1200 = ₹750 (the other share is ₹450)
Join a : b and b : c
scale both so the shared term matches
A : B = 2 : 3 and B : C = 4 : 5. Find A : B : C.
Multiply the first by 4 and the second by 3: 8 : 12 : 15
Averages and mixtures
Average
sum ÷ count; so sum = average × count
5 numbers average 40. A sixth number, 70, is added. What is the new average?
(5 × 40 + 70) ÷ 6 = 45
Weighted average of two groups
(n₁a₁ + n₂a₂) ÷ (n₁ + n₂)
30 students average 60; 20 others average 70. What is the class average?
(30×60 + 20×70) ÷ 50 = 64
Alligation: mixing a cheap and a dear item to a mean price m
cheap : dear = (dear − m) : (m − cheap)
Rice at ₹40/kg is mixed with rice at ₹60/kg to sell at ₹45/kg with no gain or loss. In what ratio?
(60 − 45) : (45 − 40) = 15 : 5 = 3 : 1
Profit, loss and discount
Profit per cent
(SP − CP) ÷ CP × 100
Bought for ₹400, sold for ₹460. Profit per cent?
(460 − 400) ÷ 400 × 100 = 15%
Price after a d% discount
marked price × (100 − d)/100
Marked ₹800, 15% off. Selling price?
800 × 85/100 = ₹680
Two discounts in a row
a + b − ab/100
Discounts of 20% and then 10%. What single discount is that?
20 + 10 − (20×10)/100 = 28%
Simple and compound interest
Simple interest
P × R × T ÷ 100
₹5,000 at 8% a year simple interest for 3 years. Interest?
5000 × 8 × 3 ÷ 100 = ₹1,200
Compound interest (yearly)
amount = P(1 + R/100)ⁿ; interest = amount − P
₹10,000 at 10% compounded yearly for 2 years. Interest?
10000 × (1 + 10/100)^2 − 10000 = ₹12,100 − ₹10,000 = ₹2,100
CI − SI over two years
P × (R/100)²
On ₹10,000 at 10% for two years, how much more is compound than simple interest?
10000 × (10/100)² = ₹100
Speed, time and distance
Distance
speed × time; km/h × 5/18 = m/s
What is 72 km/h in metres per second?
72 × 5/18 = 20 m/s
Average speed over two equal distances
2ab ÷ (a + b) (not (a + b)/2)
There at 40 km/h, back at 60 km/h. Average speed?
2 × 40 × 60 ÷ 100 = 48 km/h
Two objects moving towards each other
relative speed = sum of speeds
Trains 150 m and 100 m long run towards each other at 50 and 40 km/h. How many seconds to pass each other?
250 m ÷ (90 × 5/18 m/s) = 10 seconds
Time and work
Two people working together
1/a + 1/b of the job a day, so ab ÷ (a + b) days
A does a job in 10 days, B in 15. Together?
10 × 15 ÷ 25 = 6 days
Areas and volumes
Circle
area πr²; circumference 2πr (π ≈ 22/7)
Area of a circle of radius 7 cm?
22/7 × 7 × 7 = 154 cm²
Triangle
½ × base × height
Area of a triangle with base 12 cm and height 9 cm?
½ × 12 × 9 = 54 cm²
Cylinder
volume πr²h
Volume of a cylinder, radius 7 cm, height 10 cm?
22/7 × 7² × 10 = 1540 cm³
Mean and median
Mean and median
mean = sum ÷ count; median = middle value once sorted
For 14, 3, 9, 4, 10: by how much does the median exceed the mean?
Sorted: 3, 4, 9, 10, 14, so the median is 9; the mean is 8; the difference is 1
Data interpretation: a table: library visitors
Visitors (in thousands) to the four public libraries of Sundarvan district, an illustrative district.
| Library | 2023 | 2024 | 2025 |
|---|---|---|---|
| North | 48 | 54 | 60 |
| South | 36 | 45 | 42 |
| East | 25 | 30 | 40 |
| West | 51 | 51 | 58 |
By what percentage did visitors to East rise from 2023 to 2025?
(40 − 25) ÷ 25 × 100 = 60%
What share of all 2024 visitors went to North?
2024 total = 54 + 45 + 30 + 51 = 180; 54 ÷ 180 × 100 = 30%
What was South’s average yearly footfall over the three years, in thousands?
(36 + 45 + 42) ÷ 3 = 41 thousand
By what percentage did total visitors change from 2024 to 2025?
Totals: 180 in 2024, 200 in 2025; (200 − 180) ÷ 180 × 100 = 11.11%
Which library grew fastest, in percentage terms, from 2023 to 2025?
North 25%, South 16.67%, East 60%, West 13.73%: East grew fastest.
Figures are illustrative.
Data interpretation: a passage: a school budget
In an illustrative year, Vindhya Pradesh budgeted ₹2,400 crore for school education. Teacher salaries took 45%, mid-day meals 20% and buildings 15%. The rest went to books and digital learning, in the ratio 3 : 2. The mid-day meal scheme fed 4,00,000 children.
How much went to books, in crore?
The rest is 20% of 2400 = 480 crore; books get 3/5 of that = 288 crore
What did the mid-day meal scheme spend per child, in rupees?
20% of 2400 crore = 480 crore = ₹4,80,00,00,000; ÷ 4,00,000 children = ₹12,000
If next year’s budget rises 10% and salaries keep a 45% share, by how many crore do salaries rise?
45% of 2640 − 45% of 2400 = 1188 − 1080 = 108 crore
Figures are illustrative.
Questions
What maths does CLAT Quantitative Techniques test?
Class 10 arithmetic applied to passages, tables and charts: percentages, ratios, averages, profit and loss, interest, speed and work, and basic areas. The section carries 10–14 questions.
Can I use a calculator in CLAT?
The CLAT 2026 question booklet prohibited electronic devices in the test premises, naming mobile phones, headphones, digital watches. Plan to calculate by hand, with rough work in the booklet; check your CLAT 2027 admit card for this year's rules.
Which formulas matter most for CLAT quant?
Percentage change, percentage points, ratios and averages come up in almost every data set. Learn the fraction-to-percentage table: it turns most divisions into recognition.
