Calculation speed: the fraction, square and table values worth memorising

There is no calculator in IBPS PO prelims, and none at all in RRB NTPC. You have twenty minutes for thirty-five quantitative questions, roughly a third of which are data interpretation involving percentages of awkward numbers. The candidates who finish that section are not doing long division faster. They are not doing long division at all.

The fraction table, which is the highest-value thing on this page

Almost every percentage in a data interpretation set is close to a simple fraction. Recognising which one converts a division into a multiplication you can do in your head.

Fraction	Percentage	Fraction	Percentage
1/2	50%	1/12	8.33%
1/3	33.33%	1/13	7.69%
1/4	25%	1/14	7.14%
1/5	20%	1/15	6.67%
1/6	16.67%	1/16	6.25%
1/7	14.29%	1/18	5.56%
1/8	12.5%	1/20	5%
1/9	11.11%	1/24	4.17%
1/10	10%	1/25	4%
1/11	9.09%	1/30	3.33%

Multiples matter as much as the base values. Learn these as families:

• Sixths: 16.67, 33.33, 50, 66.67, 83.33
• Sevenths: 14.29, 28.57, 42.86, 57.14, 71.43, 85.71
• Eighths: 12.5, 25, 37.5, 50, 62.5, 75, 87.5
• Ninths: 11.11, 22.22, 33.33, 44.44, 55.56
• Elevenths: 9.09, 18.18, 27.27, 36.36, 45.45
• Twelfths: 8.33, 16.67, 25, 33.33, 41.67

How you actually use it. Suppose a set asks for 37.5% of 4,896. Long multiplication is slow. But 37.5% is 3/8, so the calculation is 4,896 ÷ 8 = 612, then × 3 = 1,836. That is five seconds of mental arithmetic against forty of written work.

Or the reverse direction, which is more common in data interpretation. “Production rose from 640 to 720. What is the percentage increase?” The increase is 80, and 80/640 = 1/8, which is 12.5%. No division performed at all.

Squares to thirty, and the ones beyond that recur

n	n²	n	n²	n	n²
11	121	18	324	25	625
12	144	19	361	26	676
13	169	20	400	27	729
14	196	21	441	28	784
15	225	22	484	29	841
16	256	23	529	30	900
17	289	24	576	35	1225

Also worth having instantly: 40² = 1600, 45² = 2025, 50² = 2500, 60² = 3600, 75² = 5625, 80² = 6400, 90² = 8100.

Cubes to fifteen: 1728, 2197, 2744, 3375 for 12 to 15, on top of the smaller ones you already know. These appear constantly in number series questions, where recognising 2,744 as 14³ is the entire question.

Two squaring tricks that are genuinely fast

Numbers ending in 5. Take the digits before the 5, multiply by the next integer up, and append 25.

• 35²: 3 × 4 = 12, so 1225.
• 65²: 6 × 7 = 42, so 4225.
• 95²: 9 × 10 = 90, so 9025.

Numbers near a round base. Use (a ± b)² = a² ± 2ab + b².

• 98² = 10,000 − 400 + 4 = 9,604.
• 103² = 10,000 + 600 + 9 = 10,609.
• 47² = 2,500 − 300 + 9 = 2,209.

Multiplication tables to twenty

Everyone knows tables to ten and almost nobody has eleven to twenty genuinely instant. That gap costs real time, because two-digit multiplication appears in nearly every arithmetic question.

The ones most worth drilling are 12, 14, 15, 16 and 25, because they show up disproportionately: 12 for dozens and months, 15 for time and percentage work, 16 for the 6.25% family, and 25 for quarters.

Percentage change, done properly

The formula candidates use is (new − old)/old × 100. The formula that is faster is recognising the ratio.

Successive changes. A 10% rise followed by a 10% fall is not zero. It is 1.1 × 0.9 = 0.99, a 1% net fall. The general shortcut for two successive percentage changes a and b, both signed:

Net change = a + b + (ab/100)

So +20% then +30% is 20 + 30 + 6 = +56%. And +20% then −20% is 20 − 20 − 4 = −4%.

Percentage to ratio, for the “how much more” questions. If A is 25% more than B, then A : B is 5 : 4, and B is 20% less than A, not 25%. This asymmetry is deliberately tested and it catches people every single time. The general rule: if A is x% more than B, then B is x/(100 + x) × 100 per cent less than A.

Approximation: read the options first

Approximation questions in prelims are explicitly asking you not to be exact. Look at the options before you calculate. If they are 1,240, 1,680, 2,150 and 2,600, then rounding every number to two significant figures is plenty. If they are 1,242, 1,246, 1,248 and 1,251, you need real precision, and that is a question to consider leaving.

A worked example. “Find the approximate value of 43.9% of 1,199 + 24.8% of 799.”

Round it: 44% of 1,200 is close to 4/9 of 1,200 = 533. And 25% of 800 = 200. Total about 733. Any option within a few units of that is the answer, and the whole thing took under ten seconds.

How to drill this

Ten minutes a day, and be specific about it:

1. Two minutes: write the fraction table from memory. Check. Repeat only the ones you missed.
2. Three minutes: twenty random two-digit squares, spoken aloud, timed.
3. Five minutes: one data interpretation set with a rule that you may not write any division. Force the fractions.

There are 55 practice questions on exactly this material, split into batches for fractions, squares, tables, percentage change and approximation. They are untimed and show the method after every answer, so use them to check that a value is genuinely on recall rather than being reconstructed each time.

Two weeks of that changes your quantitative section more than a month of learning new chapters, because it applies to every question rather than to one topic. Then test it against a timed mock and look at time per question on your result page: the calculation-heavy questions should be the ones that move first.