Arithmetic – IBPS PO Prelims Study Notes
Overview
Arithmetic forms the backbone of the Quantitative Aptitude section in IBPS PO Prelims. Roughly 10–15 questions out of 35 in this section are direct arithmetic applications or appear embedded within Data Interpretation sets. Mastery here is non-negotiable—these topics recur in every banking exam and offer quick marks if your fundamentals are solid.
The arithmetic umbrella covers Percentage, Ratio and Proportion, Average, Profit-Loss-Discount, Simple and Compound Interest, Time and Work, Time-Speed-Distance, Mixture and Alligation, Partnership, and Problems on Ages. These topics are deeply interconnected: a single question might combine percentage with ratio, or profit-loss with partnership. Your goal is fluency—solving standard problems in under 60 seconds through shortcuts and mental math.
Speed comes from recognizing problem patterns instantly and applying the right formula without hesitation. This guide distills the must-know concepts, formulas, and traps for each arithmetic sub-topic.
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Key Concepts
- **Percentage is a ratio out of 100.** Every percentage problem converts to a fraction or decimal for calculation. Know fraction equivalents cold: 25% = 1/4, 33.33% = 1/3, 12.5% = 1/8.
- **Ratio compares quantities; proportion equates two ratios.** When a ratio is given as a : b, actual values are ax and bx where x is the multiplier you must find.
- **Average = Sum ÷ Count.** Weighted average applies when groups have different sizes. The average of an arithmetic progression equals the middle term.
- **Profit and Loss are always calculated on Cost Price (CP).** Discount is always on Marked Price (MP). Mixing these up is the #1 error.
- **Simple Interest grows linearly; Compound Interest grows exponentially.** For 2-year problems, CI − SI = P × (R/100)².
- **Work problems are rate problems.** If A completes work in 10 days, A's rate = 1/10 work per day. Add rates when working together.
- **Speed = Distance ÷ Time.** Relative speed adds when objects move toward each other, subtracts when moving in the same direction.
- **Alligation links the mean price to component prices.** The criss-cross rule gives the ratio of quantities directly.
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Formulas / Key Facts
### Percentage
- Percentage change = (Change / Original) × 100
- If a value increases by R%, multiply by (1 + R/100); if decreases, multiply by (1 − R/100)
- Successive changes: Net effect of a% then b% = a + b + (ab/100)