In this guide
Two candidates know exactly the same method for a profit-and-loss question. One multiplies 1.25 × 0.88 in five seconds; the other writes it out and takes twenty-five. Across a paper, those twenty-second gaps add up to several questions. Calculation speed isn't talent. It is a small set of memorised facts and simple techniques, practised daily until they become automatic.
What to memorise
| Item | Range |
|---|---|
| Multiplication tables | Up to 20 |
| Squares | Up to 30 (ideally 50) |
| Cubes | Up to 15 |
| Square roots | √2 ≈ 1.414, √3 ≈ 1.732, √5 ≈ 2.236 |
| Fraction–percentage equivalents | 1/2 to 1/20 |
Multiplication shortcuts
Multiplying by 5, 25 and 125
- × 5 = × 10 ÷ 2 → 468 × 5 = 4,680 ÷ 2 = 2,340.
- × 25 = × 100 ÷ 4 → 64 × 25 = 6,400 ÷ 4 = 1,600.
- × 125 = × 1,000 ÷ 8 → 48 × 125 = 48,000 ÷ 8 = 6,000.
Multiplying by 11
For a two-digit number, write the two digits with their sum in between (carrying if needed).
- 34 × 11 → 3 (3 + 4) 4 = 374.
- 78 × 11 → 7 (15) 8 → carry the 1 → 858.
Multiplying by 9, 99 and 999
- 47 × 99 = 47 × 100 − 47 = 4,653.
Numbers near 100
To multiply 97 × 94: the deficits from 100 are 3 and 6.
Cross-subtract: 97 − 6 = 91. Multiply the deficits: 3 × 6 = 18. Answer: 9,118.
For 104 × 107: surpluses 4 and 7. 104 + 7 = 111; 4 × 7 = 28. Answer: 11,128.
Squares
Numbers ending in 5
For n5², multiply n by (n + 1) and append 25.
- 65² → 6 × 7 = 42 → 4,225.
- 115² → 11 × 12 = 132 → 13,225.
Numbers near 50
For (50 + a)² = 2,500 + 100a + a².
- 53² = 2,500 + 300 + 9 = 2,809.
- 47² = 2,500 − 300 + 9 = 2,209.
Using (a + b)²
- 104² = 10,000 + 800 + 16 = 10,816.
Division and fractions
- Divide by 5 by multiplying by 2 and shifting the decimal: 365 ÷ 5 = 73.
- Compare fractions by cross-multiplying: 7/9 vs 11/14 → 7 × 14 = 98 and 11 × 9 = 99, so 11/14 is larger.
Percentage shortcuts
- 18% of 450 = 10% (45) + 8% (36) = 81.
- x% of y = y% of x: 16% of 25 = 25% of 16 = 4.
- Successive percentages: × 1.2 × 0.9 = × 1.08 → an 8% net increase.
Checking answers with digit sums
The digit sum (repeated until one digit) of a product equals the digit sum of the product of the factors' digit sums.
Check 47 × 23 = 1,081: digit sums 4 + 7 → 11 → 2, and 2 + 3 = 5. 2 × 5 = 10 → 1. For 1,081: 1 + 0 + 8 + 1 = 10 → 1. ✓
This quickly eliminates wrong options in simplification questions.
Approximation
- Round to convenient numbers and adjust: 49.7 × 20.2 ≈ 50 × 20 = 1,000.
- Check how close the options are before choosing how precisely to calculate.
A 20-minute daily drill
| Minutes | Drill |
|---|---|
| 0–5 | 20 multiplications (2-digit × 2-digit) |
| 5–10 | 10 squares and 5 cubes from memory |
| 10–15 | 10 percentage calculations |
| 15–20 | 5 simplification questions from previous papers |
Track your time weekly. Most candidates see a clear improvement within a month.
Practice
- 76 × 25
- 67 × 11
- 96 × 93
- 85²
- 58²
- Which is larger: 5/7 or 8/11?
- 24% of 350
Answers: 1. 1,900. 2. 737. 3. 8,928. 4. 7,225. 5. 3,364. 6. 8/11 (5 × 11 = 55 < 8 × 7 = 56). 7. 84.
A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Staff Selection Commission website .
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