Arithmetic Word Problems Questions for SBI PO

Percentage and Percentage Change

Percentage is the foundation of almost every other arithmetic topic. If you are weak here, every downstream topic suffers. SBI PO loves questions where a value increases then decreases (or vice versa) by given percentages, and asks for the net effect. The key trap is assuming a 20% rise followed by a 20% fall returns to the original — it does not.

• Percentage change = (Change / Original) x 100
• Successive change formula saves time when two changes happen one after another
• For a value increased by a% then decreased by b%, net change = a - b - (ab/100) percent
• To find original value when final value and % change are known, work backwards by dividing by the multiplier
• Fraction-percentage equivalents (1/8 = 12.5%, 1/6 = 16.67%, 3/8 = 37.5%) save 30 seconds per question

Profit, Loss and Discount

SBI PO frequently combines profit-loss with successive discounts, false weights, or two-article scenarios. The trick is always to fix cost price as the base (100%) and build upward. Marked Price, Cost Price, and Selling Price form a triangle — know the relationship between all three before the exam.

• Profit% = (Profit / CP) x 100; Loss% = (Loss / CP) x 100 — always on CP
• SP = CP x (100 + Profit%) / 100
• Discount is always calculated on Marked Price, not CP
• When a trader uses a false weight, effective gain% = (True weight - False weight) / False weight x 100
• If two items sold at same SP — one at x% profit and one at x% loss — there is always a net loss of (x squared / 100)%

Simple Interest and Compound Interest

SI questions are usually straightforward rate or time finders. CI questions in SBI PO are trickier — they test difference between CI and SI for 2 or 3 years, or mixing of installments. For 2-year problems, the difference between CI and SI equals P(r/100)^2, which is a massive shortcut. Compound interest compounded half-yearly means rate is halved and time is doubled.

• SI = PRT/100; CI = P[(1 + r/100)^n - 1]
• Difference between CI and SI for 2 years = P(r/100)^2
• For 3 years, CI - SI = P(r/100)^2 x (r/100 + 3)
• Half-yearly compounding: use r/2 as rate and 2n as time
• If CI for 2 consecutive years is given, their ratio directly gives (1 + r/100)

Time, Speed and Distance

SBI PO tests TSD through trains, boats, circular tracks, and relative speed. The golden rule is: when two objects move toward each other, add speeds; when moving same direction, subtract. For trains, always add lengths when crossing each other. Boats upstream and downstream problems use a standard pair of equations — memorise the average speed formula for equal distance trips.

• Speed = Distance / Time; keep units consistent always
• Relative speed (opposite): S1 + S2; Relative speed (same): |S1 - S2|
• Average speed for equal distances = 2ab / (a+b), not simple average
• Boat: Downstream = u + v; Upstream = u - v; where u = boat speed, v = stream speed
• Time to cross a platform = (Length of train + Length of platform) / Speed of train

Time and Work

In SBI PO mains, Time and Work appears with pipes-cisterns blended in or with efficiency ratios. The LCM method is the fastest approach: assume total work = LCM of all given days, compute per-day work for each person, then add or subtract. Pipes follow the same logic — filling pipes add, leaking pipes subtract.

• LCM Method: Total Work = LCM of days; Efficiency = Total Work / Days taken
• If A does work in a days and B in b days, together they finish in ab/(a+b) days
• Wages are distributed in ratio of work done (efficiency x time worked)
• A can do work in x days means A does 1/x of work per day
• If a pipe fills a tank in h hours, it fills 1/h of the tank per hour

Ratio, Proportion and Mixtures

Mixture problems (alligation) appear in almost every SBI PO prelim. Alligation is a cross-subtraction method that finds the ratio in which two ingredients must be mixed to achieve a desired mean value. It works for price, percentage, speed — any parameter. Just draw the alligation diagram and cross-subtract.

• Alligation Rule: (Quantity of Cheaper) / (Quantity of Dearer) = (Dearer price - Mean price) / (Mean price - Cheaper price)
• If ratios change after adding or removing a component, set up simultaneous equations or use unitary method
• Compound ratio = product of individual ratios
• Componendo-Dividendo: if a/b = c/d, then (a+b)/(a-b) = (c+d)/(c-d) — saves steps in proportion problems
• In replacement problems: final concentration = C x (1 - r/T)^n where r = replaced quantity, T = total, n = times

• Calculating profit or loss percentage on Selling Price instead of Cost Price — the formula always uses CP as base.
• Using simple average speed instead of harmonic mean (2ab/a+b) when same distance is covered at two speeds — classic SBI PO trap.
• Forgetting to add train lengths when two trains cross each other, or adding only one train length when crossing a pole.
• In CI problems, applying the standard formula without adjusting for half-yearly compounding — r becomes r/2 and n becomes 2n.
• In ratio/mixture problems, assuming the total ratio parts equal the actual quantity — always check if a multiplier is needed.

• PDST Triangle: Profit on CP, Discount on MP, SP connects both — never mix up the base.
• SAD for boats: Speed of boat = Average of Downstream and Upstream; Stream speed = Difference divided by 2.
• Same SP Same % = Always a Loss, Loss% = x-squared over 100 — remember Same Same Square Loss.
• For Time-Work use the LCM Lifeline: assume LCM as total work, efficiencies become whole numbers, no fractions to deal with.
• Alligation cross diagram: Write cheap on left, dear on right, mean in centre — cross-subtract diagonally to get ratio.

• SBI PO prelims usually has 10-12 arithmetic word problems — target 8 correct in 12 minutes. Do not spend more than 90 seconds on any single question.
• Recent SBI PO papers (2023-2024) heavily featured two-variable mixture problems and compound interest with different compounding periods — practice these specifically.
• In mains descriptive and DI sets, word problems appear as embedded questions. Misreading the condition (e.g., marked price vs cost price) costs full marks, so underline key terms.
• Approximation is your friend in prelims — SBI PO options are usually spaced enough that rounding to nearest integer or 0.5 gives the right answer without full calculation.
• Difficulty in SBI PO is slightly higher than IBPS PO — expect at least 2-3 questions that combine two topics (e.g., SI and ratio together, or speed and work). Recognise the hybrid type quickly and decide whether to attempt or skip.