Arithmetic Questions for SBI PO

Percentage & Ratio Fundamentals

Percentage is a fraction with denominator 100. In SBI PO, percentage questions often hide inside word problems about discounts, markups, or population changes. Ratio is a comparison between two quantities. The key insight: percentage and ratio are interchangeable tools. If A is 25% more than B, then A:B = 5:4. Master this conversion and half your percentage problems become ratio problems (which are often faster to solve). SBI loves mixing percentage with profit-loss or comparing two scenarios.

• Percentage = (Part / Whole) × 100; always identify what is part and what is whole
• Ratio A:B = 3:5 means A = 3x, B = 5x for some value x; use this to avoid fractions
• Percentage increase/decrease: New = Old × (1 ± r/100); r is the percentage
• If A is p% more than B, then A/B = (100+p)/100; use this for quick comparisons
• Successive percentage changes multiply, not add: (1 + p1/100) × (1 + p2/100)
• Reverse percentage: If final value is known, divide by the multiplier to get original

Profit, Loss & Discount

This is the most tested arithmetic topic in SBI PO. The framework is simple: Profit = Selling Price - Cost Price. But SBI twists it with multiple items, discounts on discounts, or markup scenarios. The real skill is identifying what you know and what you need to find. Always draw a quick table: Cost Price (CP), Marked Price (MP), Selling Price (SP), Profit %, Discount %. One formula ties them all: SP = MP × (1 - Discount%) and Profit% = ((SP - CP) / CP) × 100.

• Profit = SP - CP; Profit% = (Profit / CP) × 100
• Loss = CP - SP; Loss% = (Loss / CP) × 100
• Marked Price (MP) is the tag price; Discount is always on MP, not CP
• SP = MP × (1 - Discount%/100); this is the core discount formula
• Profit% is calculated on CP, not MP or SP; this is the biggest trap
• Successive discounts multiply: Final SP = MP × (1 - d1/100) × (1 - d2/100)

Simple & Compound Interest

Interest questions appear in 2-3 SBI PO papers per year. Simple Interest (SI) is linear; Compound Interest (CI) is exponential. The difference grows with time. SI is rarely asked alone; SBI usually asks SI vs CI comparison or CI with different compounding periods. Key insight: CI for 2 years = SI for 2 years + SI on first year's interest. This helps you estimate CI quickly without memorizing the formula.

• SI = (Principal × Rate × Time) / 100; grows linearly
• CI = Principal × (1 + Rate/100)^Time - Principal; grows exponentially
• Amount = Principal + Interest (for both SI and CI)
• CI - SI for 2 years = (Principal × Rate^2) / 100^2; useful for quick comparison
• When compounding is half-yearly or quarterly, adjust rate and time: divide rate by 2 or 4, multiply time by 2 or 4
• For CI, if rate is given as 'p% per annum compounded half-yearly', use p/2 as rate and 2t as time periods

Time, Work & Rates

Work problems test your ability to convert word descriptions into equations. The core idea: Work = Rate × Time. If A completes a job in 10 days, A's rate is 1/10 of the job per day. When A and B work together, their rates add. SBI often mixes this with pipes-and-tanks or partial work scenarios. The trick: always think in terms of 'fraction of work per unit time', not absolute time.

• If A completes work in 'a' days, A's rate = 1/a of work per day
• If A and B work together, combined rate = 1/a + 1/b; time to complete = 1 / (combined rate)
• If A works for x days and B for y days on the same job, then (x/a) + (y/b) = 1 (total work)
• Pipes: inflow rate is positive, outflow rate is negative; net rate = inflow - outflow
• For partial work: if A does 1/3 of job and B does 2/3, time depends on their individual rates
• Efficiency ratio: if A is twice as efficient as B, A completes in half the time; rates are in ratio 2:1

Average & Mixture

Average problems in SBI PO often involve weighted averages or finding missing values. The formula is simple: Average = Sum / Count. But SBI twists it: 'Average age of 5 people is 30. One person leaves, average becomes 28. Find the person's age.' This requires you to work backwards from average to sum. Mixture problems are similar: if you mix two quantities with different values, the resulting average lies between them, weighted by quantity.

• Average = Sum of all values / Number of values; rearrange to find missing values
• Weighted average: if m items have value a and n items have value b, average = (m×a + n×b) / (m+n)
• When average changes after adding/removing an item: new sum = new average × new count
• Alligation method: for mixture problems, use the average as a pivot; differences from average are inversely proportional to quantities
• If average of n numbers is A and one number is replaced, new average = A + (new - old) / n
• For consecutive numbers, average = (first + last) / 2

• Confusing profit% calculation base: profit% is always on CP, not on SP or MP. If SP = 100 and profit = 20, CP = 100/1.20 = 83.33, NOT 80.
• Treating successive discounts as additive: 20% + 10% discount is NOT 30%. It's (1-0.20)×(1-0.10) = 0.72, so 28% total discount.
• Forgetting to adjust rate and time for half-yearly/quarterly compounding: if 12% p.a. compounded half-yearly, use 6% per half-year, not 12%.
• In work problems, adding times instead of rates: if A takes 6 days and B takes 3 days, together it's NOT 9 days. Rates are 1/6 + 1/3 = 1/2, so 2 days.
• Misidentifying what percentage is calculated on: discount is on MP, profit% is on CP, markup is on CP. Read carefully which price is the base.

• CPMSSP: Cost Price, Marked Price, Selling Price, Profit/Loss, Profit%. This is the hierarchy; always identify each in a problem.
• SI is Linear, CI is eXponential: SI grows like a straight line (same interest every year), CI grows like a curve (interest on interest).
• Rates ADD when working together: A's rate + B's rate = combined rate. This is the mental model for all work problems.
• Percentage Conversion: If A is 25% more than B, then A:B = 5:4 (add 25 to 100 = 125, ratio is 125:100 = 5:4). Reverse: 4:5 ratio means 25% more.

• SBI PO Quant has 35 questions in 20 minutes. Arithmetic is 8-12 of these. Spend max 90 seconds per question; if stuck, move on. Arithmetic is often easier than DI, so prioritize it for quick marks.
• Recent SBI papers (2023-24) show a trend: 1-2 questions mixing profit-loss with percentage or ratio. Example: 'A shopkeeper marks goods 40% above CP, gives 10% discount, and makes 26% profit. Find CP.' Requires chaining three concepts.
• Word problems dominate; pure formula questions are rare. Read carefully for hidden information: 'A works 2 days, then B joins' is different from 'A and B work together'. Underline numbers and relationships.
• Compound interest questions often ask for 'difference between CI and SI' rather than absolute CI. This is faster to calculate using the formula CI - SI = PR^2/10000 for 2 years.
• Time management: if a problem involves more than 3 steps or fractions, consider if there's a ratio/proportion shortcut. SBI rewards speed; the fastest solvers use mental math and avoid calculators for simple arithmetic.