Think of simplification as the act of collapsing a tangled expression into a single clean number. The exam gives you something that looks messy — brackets inside brackets, a mix of division and multiplication, a percentage layered on top of a fraction — and your job is to untangle it systematically, without making a single order-of-operations error.
Approximation is the sibling skill: instead of computing exactly, you round each number to a friendlier value, calculate fast, and pick the option closest to your result. The two skills together cover a large chunk of the Quant section in IBPS RRB Officer Scale I.
Here is an analogy that sticks. Imagine you are the cashier at a सहकारी बैंक (cooperative bank) counter on a busy Monday. A farmer places a mix of coins, notes, and a cheque on your desk. Simplification is counting everything in the correct sequence — coins first, then notes, then cheque — so you don't double-count or miss anything. Approximation is quickly estimating whether the farmer has "roughly ₹500" so you can tell him whether his deposit clears a minimum balance, without counting every coin down to the paisa.
Both skills reward structured thinking, not raw computation speed. You should not be calculating faster — you should be calculating less, by choosing the right method before you touch the numbers.
One more framing worth keeping: in a paper where every second matters, a simplification question that looks like "just arithmetic" is actually a trap for candidates who abandon structure under time pressure. The candidate who applies BODMAS mechanically and reads percentage questions as fraction conversions will outpace the one who tries to hold everything in working memory.
BODMAS is the sequence in which you resolve operations inside an expression:
B → O → D → M → A → S
| Letter | Stands for | What it means |
|--------|-----------|---------------|
| B | Brackets | Innermost bracket first: ( ) before { } before [ ] |
| O | Orders | Powers and roots: x², √x, xⁿ |
| D | Division | Left to right |
| M | Multiplication | Left to right (same priority as D) |
| A | Addition | Left to right |
| S | Subtraction | Left to right (same priority as A) |
Critical detail most candidates miss: Division and Multiplication have equal priority, resolved left to right. Same for Addition and Subtraction. So in 36 ÷ 4 × 2, you do 36 ÷ 4 = 9 first (leftmost), then 9 × 2 = 18. You do not first compute 4 × 2 = 8 and then 36 ÷ 8 = 4.5. That's the trap.
When you have nested brackets, start from the innermost and peel outward:
[{(3 + 2) × 4} - 6] ÷ 2
Step 1: Inner ( ): 3 + 2 = 5
Step 2: { }: 5 × 4 = 20, then 20 - 6 = 14
Step 3: [ ]: Already resolved to 14
Step 4: 14 ÷ 2 = 7
Never skip steps by trying to resolve multiple brackets simultaneously in your head.
For indices: 2³ = 8, 3² = 9, 5⁰ = 1. These come before any other arithmetic operation (after brackets).
For surds (square roots): √144 = 12, √225 = 15, √400 = 20. Build a mental table up to √625 = 25. The exam rarely goes beyond √900 = 30.
Key identity to remember: (a + b)² = a² + 2ab + b² and (a - b)² = a² - 2ab + b². These let you skip expansion when the expression has a recognizable pattern.
Convert common percentages to fractions before calculating, not after:
| Percentage | Fraction | |-----------|----------| | 12.5% | 1/8 | | 25% | 1/4 | | 33.33% | 1/3 | | 37.5% | 3/8 | | 40% | 2/5 | | 62.5% | 5/8 | | 66.67% | 2/3 | | 75% | 3/4 | | 87.5% | 7/8 |
Look — 12.5% of 800 becomes 800 × (1/8) = 100. That's one step. The long route — 0.125 × 800 — takes three times as long and invites decimal errors.
Approximation questions give you messy decimals and ask you to pick the nearest option. The rule: round each number to the nearest integer (or nearest 5/10 for large numbers), compute, then scan the options.
Important discipline: round all numbers in the same direction (all up or all down) only when the expression is purely additive or subtractive. When the expression has multiplication or division, rounding both the numerator and denominator upward can compound errors. Instead, round one up and one down to cancel bias.
For example, 47.8 + 23.2 - 16.9:
47.8 → 48 (round up by 0.2)23.2 → 23 (round down by 0.2)16.9 → 17 (round up by 0.1)Net rounding error: +0.2 - 0.2 - 0.1 = -0.1 — negligible. Result: 48 + 23 - 17 = 54. Actual: 54.1. Match.
When a question asks "P% of X + Q% of Y", convert both percentages to fractions, compute each term separately, then add. Do not combine the percentages unless X = Y.
25% of 240 + 40% of 150
= (1/4) × 240 + (2/5) × 150
= 60 + 60
= 120
When you see Division and Multiplication (or Addition and Subtraction) adjacent in an expression, lock in a left-to-right scan before computing anything. Draw a small arrow → above the expression in your rough work to remind yourself. Example: 36 ÷ 4 × 2 — arrow forces you to do 9 × 2 = 18, not 36 ÷ 8 = 4.5. This single habit eliminates the most common BODMAS error. Standard method (guessing order): 2-3 errors per 10 questions. With arrow habit: near zero. Step count same, but accuracy jumps sharply.
Memorize the 9 key fraction-percentage pairs (12.5% = 1/8, 25% = 1/4, etc.) and substitute before touching the calculator. When a percentage question has a number divisible by the denominator of the equivalent fraction, the multiplication becomes trivial division. Example: 37.5% of 480 → substitute 3/8 × 480 = 3 × 60 = 180. Standard decimal route: 0.375 × 480 requires multi-digit multiplication (roughly 45 seconds). Fraction route: 8 seconds. Step count drops from 4 to 2.
For approximation with addition/subtraction of 3+ numbers, note which numbers you rounded up and which you rounded down. If the ups and downs roughly cancel, your result is reliable. If they don't cancel (e.g., you rounded everything up), subtract roughly half the total rounding from your answer before checking options. This lets you avoid re-computing. Example: 149.8 + 251.3 + 98.6 — rounding: 150 + 251 + 99 = 500. Rounding errors: +0.2 - 0.3 + 0.4 = +0.3. So actual ≈ 500 - 0.3 = 499.7. Pick 500 from options. Standard approach (computing exactly): 60 seconds. Bias-cancellation check: 20 seconds.
Split an awkward percentage into two clean parts. Example: 17.5% of 400 — split into 10% + 7.5% = 40 + 30 = 70. Or 22% of 350 — split into 20% + 2% = 70 + 7 = 77. This avoids multiplying by ugly decimals entirely. Standard method (0.175 × 400): requires careful decimal arithmetic, 40 seconds. Split method: 15 seconds, 3 mental steps vs 6.
Before computing √x, check if x is a perfect square or close to one. Build the ladder: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225. For approximation questions with surds, identify the two perfect squares the number falls between. √170 lies between √169 = 13 and √196 = 14, so it is just above 13. Pick the option closest to 13. Standard approach (long division): 90 seconds. Perfect square ladder: 10 seconds.
In the exam hall, when you see a simplification or approximation question, run this decision tree before writing anything:
Step 1 — Classify the question type.
Step 2 — Spot the shortcut before computing.
Step 3 — Compute in stages, write each intermediate result.
Never hold more than one intermediate result in your head. Write 9 × 2 = 18, then carry 18 forward. One line per step.
Step 4 — Sanity check against options. If your answer matches one option exactly, stop. If it is between two options, you made a rounding error somewhere — go back to Step 2 and re-check your rounding direction.
Target: 30-45 seconds per question for straightforward BODMAS; 20-30 seconds for pure approximation.
Why this question: Tests the O (Orders/Indices) step in BODMAS, which candidates often skip.
Solving path: Resolve indices first — 2³ = 8, 3² = 9. Then brackets: (8 + 9) = 17. Then multiply: 17 × 5 = 85. Then subtract: 85 - 40 = 45. The trap is computing 8 × 5 or 9 × 5 separately before adding — that's arithmetic algebra, not BODMAS.
Why this question: Classic approximation — all numbers have decimals, and the options are spaced 2 apart, so clean rounding works perfectly.
Solving path: Round 47.8 → 48, 23.2 → 23, 16.9 → 17. Compute 48 + 23 - 17 = 54. Bias check: +0.2 - 0.2 - 0.1 = -0.1, negligible. Option A (54) is correct.
Why this question: Tests the fraction-substitution shortcut for 12.5%, one of the most common percentage values in banking exams.
Solving path: Recognize 12.5% = 1/8. Then (1/8) × 800 = 100. If you go the decimal route, 0.125 × 800, you still get 100 but it takes 3x longer and risks a decimal shift error.
Why this question: Tests left-to-right resolution of D/M — the most commonly confused BODMAS step.
Solving path: Identify all operations: ÷, ×, +, -. Resolve D before M (but left to right): 45 ÷ 5 = 9. Then 3 × 4 = 12. Then add/subtract left to right: 9 + 12 = 21, 21 - 7 = 14. The trap option 16 comes from computing 3 × 4 - 7 = 5 first and then adding 9 + 5 = 14... wait, that's actually correct here, but the dangerous habit is ignoring the sequence — in other expressions it will fail you.
Why this question: Compound percentage — tests whether you keep the two percentage calculations separate or mistakenly add percentages first.
Solving path: 25% of 240 = (1/4) × 240 = 60. 40% of 150 = (2/5) × 150 = 60. Total = 60 + 60 = 120. The critical error to avoid: adding 25 + 40 = 65% and then applying it to some average base. Never add percentages when the bases are different.
Resolving Multiplication before Division when Division appears first on the left. In 36 ÷ 4 × 2, computing 4 × 2 = 8 first gives 36 ÷ 8 = 4.5, which is wrong. Division and Multiplication have equal priority — go left to right, always.
Ignoring the Orders step (indices and roots). In an expression like (2³ + 3²) × 5, candidates sometimes read 2³ as 2 × 3 = 6 under time pressure. Indices come after brackets, before everything else — they are not optional.
Adding percentages with different bases. 25% of 240 + 40% of 150 is NOT 65% of 390. Percentages can only be combined if the base is identical. Otherwise, compute each term separately.
Rounding all decimals in the same direction for subtraction. If you round 47.8 → 48 (up by 0.2) and also round 16.9 → 17 (up by 0.1), you have inflated the minuend and also inflated the subtrahend — these partially cancel, which is fine. But if you round 16.9 → 16 (down by 0.9) while rounding the others up, your answer will be off by nearly 1. Check your rounding direction against the operation sign.
Treating 12.5% as 1/10 instead of 1/8. This is a memorization gap that costs points. 10% = 1/10, 12.5% = 1/8. Drill the fraction table until the substitution is automatic.
Skipping intermediate write-down steps under time pressure. The time you save by not writing 9 × 2 = 18 in rough work is less than the time you lose when you make a carry error and have to recompute the whole expression. Write every intermediate result on paper.