Arithmetic Questions for IBPS PO

Percentage

Percentage is the language of banking. Every DI table, every profit-loss and every interest problem secretly uses percentages. The key skill is converting between fractions, decimals and percentages instantly without pen-work. Also master the successive change formula to avoid step-by-step multiplication.

• Learn fraction-to-percent table up to 1/12 cold: 1/8 = 12.5%, 1/6 = 16.67%, 1/7 approx 14.28%
• Percentage change = (change / original) x 100
• Successive changes of a% then b%: net = a + b + ab/100
• If A is x% more than B, then B is less than A by x/(100+x) x 100 percent
• Multiplying factor shortcut: 20% increase = multiply by 1.2; 15% decrease = multiply by 0.85

Profit, Loss and Discount

Profit-Loss questions in IBPS PO often involve dishonest dealers, false weights, or two successive transactions. The trick is always to anchor everything to Cost Price = 100 as a base. Discount works on Marked Price, not Cost Price — this distinction alone eliminates half the errors aspirants make.

• CP = 100 base trick: if profit is 20%, SP = 120, simple ratio math follows
• Discount is always on Marked Price; Profit is always on Cost Price
• False weight formula: 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: always a net LOSS of x²/100 percent
• Overall profit when buying at a% less and selling at b% more: combined factor = (1 - a/100)(1 + b/100)

Simple Interest and Compound Interest

SI and CI appear almost every year in IBPS PO, often asking for the difference between SI and CI for 2 or 3 years or finding rate/time. For 2 years, the difference between CI and SI equals P x (r/100)². Memorise this — it saves 40 seconds per question. For 3 years learn the expanded difference formula.

• SI = PRT/100; CI uses A = P(1 + r/100)^n
• Difference CI - SI for 2 years = P(r/100)²
• Difference CI - SI for 3 years = P(r/100)² x (r/100 + 3)
• When compounding is half-yearly: rate halves, time doubles
• If CI for 2nd year is given alone it already includes interest on first year interest — use it to find rate

Ratio, Proportion and Mixtures

Ratio questions appear in partnerships, ages, and mixtures. The alligation method is the fastest tool for mixtures and average-based problems. Think of it as a cross-subtraction on a number line. It works for mixing two solutions, combining two groups with different averages, or even finding ratio of time spent at different speeds.

• Alligation cross: draw two values on top, mean in middle, cross-subtract downward
• Ratio of mixing = (higher value - mean) : (mean - lower value)
• Partnership profit split is always in ratio of capital x time
• Compounded ratio: a:b and c:d gives ac:bd
• Componendo-Dividendo: if a/b = c/d then (a+b)/(a-b) = (c+d)/(c-d) — saves steps in proportion chains

Time, Work and Pipes

The unifying concept is work rate = 1/days. Always convert everyone to per day work and add. For pipes, filling is positive, leaking is negative. IBPS PO loves questions where one person leaves midway or a pipe is opened after a delay.

• If A does work in a days, A's 1-day work = 1/a
• Combined rate of A and B = 1/a + 1/b; total days = ab/(a+b)
• Efficiency ratio is inverse of time ratio
• If A and B together finish in x days and A alone in a days, B alone = ax/(a-x)
• Pipes: if inlet fills in p hours and outlet drains in q hours, net = 1/p - 1/q

Time, Speed and Distance

TSD questions in IBPS PO often involve trains (crossing problems), boats (upstream/downstream), or average speed traps. The average speed trap is the most common wrong answer bait — average speed is NOT simple average of two speeds when equal distances are covered.

• Speed = Distance / Time; keep units consistent (km/hr vs m/s: multiply by 5/18 to convert km/hr to m/s)
• Trains crossing: length of both trains added to distance
• Boat: downstream = u+v, upstream = u-v where u = boat speed, v = current speed
• Average speed for equal distances at s1 and s2 = 2s1s2/(s1+s2), NOT (s1+s2)/2
• Relative speed: same direction = difference; opposite direction = sum

• Using simple average instead of harmonic mean for average speed when equal DISTANCES are covered — this is the most popular trap in IBPS PO TSD questions.
• Applying discount percentage on Cost Price instead of Marked Price when calculating final selling price.
• Forgetting to add both train lengths in crossing problems — only the moving object's length matters when passing a pole, BOTH lengths matter when crossing each other.
• In CI problems, treating the rate as annual when the question says half-yearly — remember to halve rate and double time.
• In partnership problems, ignoring the time component and dividing profit in simple capital ratio when partners joined at different months.

• PDST anchor: Profit on CP, Discount on MP, SI on Principal, Tax on SP — four different bases, four traps.
• For CI-SI difference in 2 years remember P-R-squared: P times (R/100) squared. Think P-R² like Pressure times Radius squared in physics.
• Alligation visual: draw a V shape. Top left = cheap price, top right = costly price, bottom point = desired mean. Cross subtract to get ratio of cheap to costly.
• Speed conversion anchor: 18 km/hr = 5 m/s. So divide by 3.6 or multiply by 5/18. Remember 18 and 5 are multiples of the same family: 18 x 5 = 90, clean number.

• IBPS PO Prelims usually has 5-7 arithmetic standalone questions plus arithmetic embedded in 2-3 DI sets. Total arithmetic exposure can be 12-15 marks out of 35.
• In Mains, arithmetic word problems appear in the 1-2 mark range and often combine two concepts — e.g. a mixture problem that also involves profit percentage. Identify the primary concept first.
• Questions on CI and percentage are the most time-efficient — they can be solved in under 60 seconds with formula shortcuts. Solve these first and bank easy marks.
• If a question gives you three or more unknowns in a ratio chain, assign the LCM of all denominators as total work or total quantity — this avoids fractions entirely.
• Recent IBPS PO papers (2022-2024) have increased data sufficiency and quantity comparison questions built on arithmetic. Practice identifying which formula is needed without solving fully — partial work earns the answer faster in such question types.