Faster calculation for IBPS Clerk

Calculation speed is the skill underneath simplification, approximation, DI and every arithmetic chapter. In the prelims you get 35 quant questions in a 20-minute sectional timer, which is a little over half a minute each. A candidate who multiplies 98 × 97 in four seconds and one who needs twenty are solving different exams.

The shortcuts below are not magic. Each one is ordinary algebra arranged so you can do it in your head. Knowing why a shortcut works matters for two reasons: you will remember it longer, and you will know when it does not apply. None of them help unless you practise until they are automatic, so there is a drill at the end.

Multiplying numbers near 100

Find how far each number is from 100, then:

• Left part = one number plus the other's distance from 100 (a surplus adds, a deficit subtracts).
• Right part = the product of the two distances, written as two digits.

Why it works: (100 − a)(100 − b) = 100(100 − a − b) + ab. The left part is the hundreds, the right part is ab.

• 98 × 97: deficits 2 and 3. Left = 98 − 3 = 95. Right = 2 × 3 = 06. Answer 9,506.
• 104 × 106: surpluses 4 and 6. Left = 104 + 6 = 110. Right = 24. Answer 11,024.
• 102 × 97: one up 2, one down 3. Left = 102 − 3 = 99, giving 9,900. Right = 2 × (−3) = −6. Answer 9,900 − 6 = 9,894.

The right part always takes two digits: write 06, not 6.

Squares near 50

For 50 + n: left part = 25 + n, right part = n² as two digits.

Why it works: (50 + n)² = 2,500 + 100n + n² = 100(25 + n) + n².

• 52²: 25 + 2 = 27, 2² = 04. Answer 2,704.
• 47²: 25 − 3 = 22, 3² = 09. Answer 2,209.

Squares ending in 5

Multiply the tens digit by the next number, then write 25.

Why it works: (10a + 5)² = 100a² + 100a + 25 = 100 × a(a + 1) + 25.

• 75²: 7 × 8 = 56, then 25. Answer 5,625.
• 115²: 11 × 12 = 132, then 25. Answer 13,225.

Multiplying by 5, 25 and 11

• × 5 = × 10 ÷ 2, because 5 = 10/2. 86 × 5 = 860 ÷ 2 = 430.
• × 25 = × 100 ÷ 4, because 25 = 100/4. 44 × 25 = 4,400 ÷ 4 = 1,100.
• Two-digit × 11: write the two digits apart and put their sum in the middle, carrying if the sum is 10 or more. This works because 11x = 10x + x.
  • 52 × 11: 5, (5 + 2), 2 = 572.
  • 78 × 11: 7, (7 + 8 = 15), 8. Carry the 1: 858.

Any two-digit product: cross multiplication

For ab × cd, work right to left:

1. Units: b × d.
2. Middle: a × d + b × c, plus any carry.
3. Left: a × c, plus any carry.

Why it works: (10a + b)(10c + d) = 100ac + 10(ad + bc) + bd.

• 23 × 41: units 3 × 1 = 3. Middle 2 × 1 + 3 × 4 = 14, write 4, carry 1. Left 2 × 4 + 1 = 9. Answer 943.

Percentages and fractions

Build any percentage from 10%, 5% and 1%, and learn the common fractions as percentages.

• 35% of 480: 10% = 48, so 30% = 144. 5% = 24. Total 168.
• 12.5% of 720 = 720 ÷ 8 = 90.

Division shortcuts

• ÷ 5 = × 2 ÷ 10: 145 ÷ 5 = 290 ÷ 10 = 29.
• ÷ 25 = × 4 ÷ 100: 350 ÷ 25 = 1,400 ÷ 100 = 14.
• ÷ 12.5 = × 8 ÷ 100: 250 ÷ 12.5 = 2,000 ÷ 100 = 20.

Checking with digit sums

Reduce each number to one digit by adding its digits, repeating until one digit is left. Do the same operation on those digits. The answer's digit sum must match.

Why it works: every number leaves the same remainder on division by 9 as its digit sum does, and remainders multiply and add the same way the numbers do.

• 98 × 97 = 9,506. 9 + 8 = 17, which gives 8. 9 + 7 = 16, which gives 7. 8 × 7 = 56, which gives 11 and then 2. The answer: 9 + 5 + 0 + 6 = 20, which gives 2. It matches.

A daily 10-minute drill

Time yourself on day 1 and again on day 14. The difference is usually large enough to convince you to keep going.

Practice

Try each without paper, then check.

1. 96 × 94
2. 103 × 107
3. 53²
4. 46²
5. 85²
6. 64 × 25
7. 34 × 21
8. 37.5% of 640

Answers:

1. 9,024. Deficits 4 and 6. Left 96 − 6 = 90, right 24.
2. 11,021. Surpluses 3 and 7. Left 103 + 7 = 110, right 21.
3. 2,809. 25 + 3 = 28, 3² = 09.
4. 2,116. 25 − 4 = 21, 4² = 16.
5. 7,225. 8 × 9 = 72, then 25.
6. 1,600. 6,400 ÷ 4.
7. 714. Units 4 × 1 = 4. Middle 3 × 1 + 4 × 2 = 11, write 1, carry 1. Left 3 × 2 + 1 = 7.
8. 240. 37.5% = 3/8, and 640 ÷ 8 × 3 = 240.

What to do next

• Run the 10-minute drill every day for three weeks.
• Learn squares to 30 and cubes to 15 by heart.
• Apply the tricks in timed sets of simplification and approximation, where they pay off most.
• Use the fraction table in data interpretation to turn percentages into quick divisions.