Read the table before the questions
Spend ten seconds on the structure: what the rows and columns are, the units (thousands? lakhs? percentages?), and any totals already given. Most mistakes come from misreading a unit or a column heading.
The five calculations
Asked for | Formula |
|---|---|
total | add the column or row |
average | total ÷ number of items |
percentage change | (new − old) ÷ old × 100 |
share of the total | part ÷ total × 100 |
ratio | divide both by their HCF |
Example data
Students enrolled in four courses:
Course | 2022 | 2023 |
|---|---|---|
A | 120 | 150 |
B | 200 | 180 |
C | 80 | 100 |
D | 100 | 130 |
Total in 2023: 150 + 180 + 100 + 130 = 560.
Growth for A: 30/120 = 25%. For D: 30/100 = 30%, the highest.
B is the only course that fell: −20/200 = −10%.
Ratio B : C in 2023 = 180 : 100 = 9 : 5.
Approximation
When the options are far apart, round the numbers. 347 out of 1,190 is about 350/1,200 ≈ 29%. If the options are 18%, 29%, 41% and 55%, you are done.
When options are close, calculate exactly, but only for the items being compared.
Comparing growth
The same absolute increase is a bigger percentage on a smaller base. A and C both grew, by 30 and 20 students, but C's 20 on a base of 80 is the same 25% as A's 30 on 120.
Shortcuts and tricks
The standard way is exact calculation: add every value, divide fully, then compare. These shortcuts trade exact arithmetic for quick estimates that still separate the options.
Average by deviation
Example: the average of 72, 68, 75, 81 and 64.
Standard way: 72 + 68 + 75 + 81 + 64 = 360, and 360 ÷ 5 = 72.
Shortcut: take 70 as a base. The deviations +2, −2, +5, +11 and −6 add to 10, so the average is 70 + 10 ÷ 5 = 72.
Fraction benchmarks
Example: 47 out of 330 as a percentage.
Standard way: 47 ÷ 330 × 100 = 14.24%.
Shortcut: 330 ÷ 7 ≈ 47, so the share is about 1/7 ≈ 14.3%. Benchmarks worth knowing: 1/6 ≈ 16.7%, 1/7 ≈ 14.3%, 1/8 = 12.5%, 1/9 ≈ 11.1%, 1/11 ≈ 9.1%.
Compare growth without dividing
Example: which grew more in percentage terms, 240 → 300 or 160 → 210?
Standard way: 60/240 = 25% and 50/160 = 31.25%, so the second.
Shortcut: compare 60/240 with 50/160 by cross-multiplying: 60 × 160 = 9,600 and 50 × 240 = 12,000. The second fraction is bigger.
Exam tips
Write the base of every percentage before dividing.
"Approximately" in a question is a hint to round.
Answer all questions on one table together; you'll reuse totals.