Approximation Tricks for DI: Percentages and Ratios Fast

DI sets in bank exams are built so that exact calculation of every question takes too long. The options, however, are usually far enough apart that a careful estimate is enough. The skill is to round in a way that keeps the error smaller than the gap between options.

The rule that keeps approximation safe: read the options before you calculate. If they are widely spread, round both numbers to friendly values. If two options are close, keep more digits for the step that decides between them.

A useful way to judge this is to think in terms of relative error. Rounding 4,812 to 4,800 changes it by about 0.25%, which is harmless when the options differ by 5% or more. Rounding 4,812 to 5,000 changes it by about 4%, which can push you onto the wrong option. As a rough guide, keep each rounding within about 1% of the original number unless the options are very far apart, and never round the same number twice in one calculation.

Approximation also helps you check exact work. If you calculate 18% of 4,250 and get 7,650, a quick estimate of "a bit under one-fifth of 4,250, so about 800" tells you immediately that a decimal point has slipped.

Any percentage can be assembled from easy blocks: 10% (move the decimal one place), 5% (half of 10%), 1% (move two places) and 50% or 25% (halve, or halve twice).

Worked example 1: 18% of 4,250

10% = 425, 5% = 212.5 and 3% = 3 × 42.5 = 127.5. Adding them: 425 + 212.5 + 127.5 = 765. Alternatively, 20% (850) minus 2% (85) gives the same answer.

Worked example 2: a percentage close to a friendly one

24.8% of 1,603 is very close to one-quarter of 1,600, which is 400. The exact value is 397.5, so the estimate is off by under 1%. That is safe unless two options lie within a few units of each other.

Many DI percentages turn out to be simple fractions in disguise. Knowing the common pairs lets you divide by recognising rather than calculating.

Fraction	Percentage	Fraction	Percentage
1/3	33.33%	1/8	12.5%
1/6	16.67%	1/9	11.11%
1/7	14.29%	1/11	9.09%
3/7	42.86%	1/12	8.33%

Each pair comes from a single division, for example 100 ÷ 7 = 14.29, so you can rebuild one you forget.

Worked example 3: spotting a fraction

What percentage is 2,856 of 6,664? Since 6,664 ÷ 7 = 952 and 952 × 3 = 2,856, the share is exactly 3/7, which is 42.86%.

For a division, round the numerator and denominator in the same direction where possible, so the errors partly cancel. Rounding one up and the other down doubles the error.

Worked example 4: a division

3,148 ÷ 789 is close to 3,150 ÷ 790, and 790 × 4 = 3,160, so the answer is just under 4. The exact value is 3.99.

"Which ratio is the highest?" questions do not need decimals at all. To compare a/b with c/d, compare the cross-products a × d and c × b.

Worked example 5: comparing two fractions

Compare 47/63 with 52/71. Cross-products: 47 × 71 = 3,337 and 52 × 63 = 3,276. The difference is 61 in favour of the first, so 47/63 is larger.

Worked example 6: estimating growth

A value rose from 4,812 to 5,390, a change of 578. 10% of 4,812 is about 481, and 578 is a little more, about 1.2 times 481. The growth is 12.01%, roughly 12%.

✘ Approximating before looking at the options, then finding two options inside your error.
✘ Rounding the numerator up and the denominator down, which stacks the errors.
✘ Converting fractions to decimals just to compare them; cross-multiply instead.
✘ Rounding the base of a percentage change more than the change itself.

Task	Quick method
x% of N	Build from 10%, 5% and 1% blocks
Percentage near a fraction	Use the fraction (12.5% = 1/8)
Division	Round both terms the same way; use a nearby multiple
Compare a/b and c/d	Compare a × d with c × b
Percentage change	Compare the change with 10% of the base

Use these with bar graphs, pie charts and tables. Bank prelims also test pure calculation in approximation and simplification; see square and cube roots and the Quant cheat code.

Q1. What is 35% of 2,460? easy

(a) 846 (b) 861 (c) 874 (d) 738

✅ Answer: (b) 861

💡 Explanation: Build it from blocks: 10% is 246, so 30% is 738, and 5% is 123. Then 738 + 123 = 861. The option 738 stops at 30%.

Q2. The fraction 1/9 is closest to which percentage? easy

(a) 9% (b) 12.5% (c) 11.11% (d) 10%

✅ Answer: (c) 11.11%

💡 Explanation: 100 ÷ 9 = 11.11, so 1/9 = 11.11%. It is worth memorising alongside 1/8 = 12.5% and 1/7 ≈ 14.29%, because DI options often sit near these values.

Q3. 4,987 ÷ 62 is approximately: medium

(a) ≈ 70 (b) ≈ 75 (c) ≈ 85 (d) ≈ 80

✅ Answer: (d) ≈ 80

💡 Explanation: Round to 4,960 ÷ 62, because 62 × 80 = 4,960. The extra 27 adds less than 1, so the answer is about 80. Rounding to 5,000 ÷ 60 gives 83, close but less accurate.

Q4. What is 12.5% of 3,368? easy

(a) 421 (b) 336.8 (c) 404 (d) 448

✅ Answer: (a) 421

💡 Explanation: 12.5% is 1/8, so divide by 8: 3,368 ÷ 8 = 421. Replacing a percentage with its fraction avoids a long multiplication.

Q5. Which is larger, 31/43 or 38/53? medium

(a) 31/43 (b) 38/53 (c) They are equal (d) Cannot be compared without a calculator

✅ Answer: (a) 31/43

💡 Explanation: Cross-multiply: 31 × 53 = 1,643 and 38 × 43 = 1,634. The first product is larger, so 31/43 is the larger fraction, though only just.

Q6. A value rose from 7,215 to 8,640. The percentage increase is approximately: medium

(a) 15% (b) 17.5% (c) 19.75% (d) 22.5%

✅ Answer: (c) 19.75%

💡 Explanation: The rise is 1,425 on a base of 7,215. 10% of the base is about 722, so 20% is about 1,443; the rise is just under that, about 19.75%.

When is it safe to approximate in a DI question?

When the gap between the options is larger than the error your rounding can create. Look at the options first: if they are 10 percent or more apart, round freely; if two are within one or two percent, keep more digits or calculate exactly.

Which fraction-to-percentage pairs are worth memorising?

The unit fractions from 1/2 to 1/12 and a few multiples: 1/3 is 33.33, 1/6 is 16.67, 1/7 is 14.29, 1/8 is 12.5, 1/9 is 11.11, 1/11 is 9.09 and 1/12 is 8.33 percent. They turn many divisions into a single look-up.

All problems and solutions on this page are original. No outside facts are relied on; every numeric answer is recomputed by software before publishing.

How this page was prepared. Drafted with AI assistance (Claude (Anthropic AI model)) from the sources listed above. 13 calculations on this page were recomputed by software and matched. Automated checks also covered structure, internal links and duplicate text. Software checks cannot confirm facts. Reviewed by praveenkumar on 2026-10-24 against the sources listed above.

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