Calculation shortcuts for SBI PO DI

In the SBI PO mains, Data Analysis & Interpretation has 30 questions for 60 marks in 45 minutes, which is two marks and 90 seconds a question. Reading a table takes a few seconds. The rest goes on arithmetic: a percentage here, a ratio there, a growth rate to compare. Candidates who know the same concepts end up with very different scores because one of them calculates twice as fast.

None of the methods below is a trick to memorise. Each one rearranges the sum into pieces you can do in your head. Learn why each works, then drill it until you reach for it without thinking.

1. Build percentages from blocks

Find 10%, 5% and 1% of the number, which are easy, and combine them.

• 17.5% of 840: 10% = 84, 5% = 42, 2.5% = 21. Total 147.
• 23.5% of 640: 20% = 128, 1% = 6.4, so 3.5% = 22.4. Total 150.4.

Why. Percentages are additive: 17.5% is 10% + 5% + 2.5% of the same base, so the parts add to the whole.

2. Know the fraction values

Many DI percentages are really fractions. Recognising them turns a division into a single step.

• 37.5% of 648 = 3/8 × 648 = 81 × 3 = 243.
• One-seventh (about 14.29%) of 350 = 350 ÷ 7 = 50.
• One-sixth (about 16.67%) of 426 = 426 ÷ 6 = 71.

3. Compare fractions without dividing

"In which year was the ratio highest?" is a standard DI question. You do not need the ratios themselves, only which one is bigger.

Cross-multiplication. To compare a/b with c/d, compare a × d with b × c.

• 37/52 vs 41/58: 37 × 58 = 2,146 and 41 × 52 = 2,132. 37/52 is larger.

Why. Multiplying both fractions by b × d (a positive number) keeps their order and clears the denominators.

Percentage-growth check. When numbers are big, compare how fast the numerator and the denominator grow from one fraction to the other.

• 342/487 vs 415/596. Numerator rises by 73 on 342, about 21%. Denominator rises by 109 on 487, about 22%.
• The denominator grows faster, so the second fraction is smaller. 342/487 is larger.
• Cross-multiplication confirms it: 342 × 596 = 203,832 and 415 × 487 = 202,105.

When the two growth rates are this close, confirm with cross-multiplication before you mark the answer.

4. Estimate division

Find a nearby multiple of the divisor, then adjust.

• 1,247 ÷ 31: 31 × 40 = 1,240, with 7 left over. 7/31 is a little over 0.2, so about 40.2.
• 2,583 ÷ 41: 41 × 60 = 2,460; the remaining 123 is 41 × 3. So 63 exactly.

Look at how far apart the options are before you calculate. If they differ by 10% or more, a rough estimate is enough.

5. Percentage change: always divide by the old value

• 64 → 80 is a rise of 16 on 64: 25%.
• 150 → 180 is a rise of 30 on 150: 20%.

The bigger absolute rise was the smaller percentage rise.

A DI-style example. A branch's deposits were 4,850 in one year and 5,720 the next. Find the percentage growth.

• Rise = 870. 10% of 4,850 = 485, so 870 is a little under 18% (18% would be 873).
• Answer: about 17.9%.

6. Successive changes

For a change of a% followed by b%, the net change is a + b + ab/100. Use negative signs for falls.

• Up 20%, then up 10%: 20 + 10 + 2 = 32%.
• Up 25%, then down 20%: 25 − 20 − 5 = 0%.
• Up 15%, then down 10%: 15 − 10 − 1.5 = 3.5%.

Why. Multiplying by 1.2 and then 1.1 gives 1.32. The ab/100 term is the second change acting on the first change.

7. Multiply fast

Two numbers near 100. Take each number's distance from 100. Cross-subtract for the first part, multiply the distances for the last two digits.

• 97 × 94: distances −3 and −6. 97 − 6 = 91; 3 × 6 = 18. 9,118.
• 108 × 107: distances +8 and +7. 108 + 7 = 115; 8 × 7 = 56. 11,556.

Squares. 104² is 104 + 4 = 108, then 4² = 16: 10,816. 96² is 96 − 4 = 92, then 16: 9,216. Near 50, add the distance to 25 and square the distance: 53² is 25 + 3 = 28, then 9: 2,809; 47² is 22, then 9: 2,209.

Why. (100 + a)(100 + b) = 100(100 + a + b) + ab. The first part is the cross-sum; the last two digits are ab.

8. Averages by deviation

Pick a round number near the middle, add up the deviations and divide only those.

• Average of 46, 53, 58, 49 and 54, taking 50: deviations −4, +3, +8, −1, +4 = +10. 10 ÷ 5 = 2, so the average is 52.

Common mistakes

• Dividing by the new value when finding percentage change.
• Estimating when the options are close. If two options differ by less than about 2%, calculate exactly.
• Adding successive percentages. Up 25% then down 20% is 0%, not +5%.
• Rounding too early. Round once, at the end.
• Not reading the unit. A table in thousands and an answer in lakh can make every option look wrong.

Practice set

1. 12.5% of 968
2. Which is larger: 45/67 or 51/76?
3. 1,836 ÷ 27
4. Net change: up 15%, then down 10%
5. 37.5% of 648
6. 108 × 107
7. 58²
8. Average of 72, 68, 75, 81 and 64

Answers:

1. 121. 968 ÷ 8.
2. 45/67, only just. 45 × 76 = 3,420; 51 × 67 = 3,417.
3. 68. 27 × 70 = 1,890; 1,890 − 54 = 1,836, so 70 − 2.
4. +3.5%. 15 − 10 − 1.5.
5. 243. 3/8 × 648.
6. 11,556. 115 then 56.
7. 3,364. 25 + 8 = 33, then 64.
8. 72. From 70: +2, −2, +5, +11, −6 = +10; 10 ÷ 5 = 2.

A daily 10-minute drill

What to do next

• Learn the fraction table until 1/7, 1/9 and 1/11 come back instantly.
• Do the 10-minute drill every day for three weeks, before your quant session.
• Apply the methods on real sets: tabular DI and simplification and approximation.