Arithmetic Word Problems Questions for RBI GRADE B

Percentage and Percentage Change

Percentage problems appear in almost every RBI Grade B paper, either standalone or embedded in DI. The core idea is expressing a part as per 100 of the whole. Percentage change problems often involve successive changes (e.g., price rises 20% then falls 10%) which trips many aspirants because changes do not simply add.

• Percentage of X = (Part / Whole) x 100
• Successive change of a% then b%: net change = a + b + (ab/100)
• If a value increases by x%, to find original: divide by (1 + x/100)
• Population or price after n years at r%: P x (1 + r/100)^n
• Fraction-to-percentage shortcuts: 1/8 = 12.5%, 1/6 = 16.67%, 1/7 approx 14.28%

Profit, Loss and Discount

Profit-loss problems link Cost Price (CP), Selling Price (SP), and Marked Price (MP). RBI Grade B often disguises these as shopkeeper problems with two successive discounts or a combination of discount and profit. Remember: discount is always on MP, but profit/loss is always calculated on CP.

• Profit% = (SP - CP) / CP x 100; Loss% = (CP - SP) / CP x 100
• SP = CP x (100 + Profit%) / 100
• Discount = MP - SP; Discount% = Discount / MP x 100
• When two articles sold at same SP, one at x% profit and other at x% loss: net result is always a loss of (x^2)/100 %
• Equivalent single discount for d1 and d2 successive: d1 + d2 - (d1 x d2)/100

Simple Interest and Compound Interest

SI and CI questions appear frequently in RBI Grade B given the banking context. The exam tests SI vs CI difference, finding principal given CI for 2 or 3 years, and effective rate of CI. The difference between CI and SI for 2 years is a very popular formula-based question. For 3 years it is slightly harder.

• SI = P x R x T / 100; Amount = P + SI
• CI Amount = P x (1 + R/100)^T
• CI - SI for 2 years = P x (R/100)^2
• CI - SI for 3 years = P x (R/100)^2 x (R/100 + 3)
• Compounding half-yearly: halve the rate, double the time

Ratio, Proportion and Mixtures (Alligation)

Ratio problems test how quantities scale together. Alligation is the shortcut for mixture problems and is extremely fast once practiced. It finds the ratio in which two ingredients at different prices (or concentrations) must be mixed to get a target. RBI DI sets sometimes embed mixture logic in data on blended products or average salaries.

• Alligation rule: (Quantity of cheaper) / (Quantity of dearer) = (Dearer - Mean) / (Mean - Cheaper)
• If A:B = m:n and B:C = p:q, then A:B:C = mp : np : nq
• In mixture replacement: after n replacements, remaining pure = P x (1 - r/P)^n where r is replaced volume
• Compounded ratio of a:b and c:d is ac:bd
• Duplicate ratio of a:b is a^2:b^2; Sub-duplicate is sqrt(a):sqrt(b)

Time, Speed and Distance

TSD problems in RBI Grade B often involve trains, boats-streams, or relative speed. The trick is to always work in consistent units (km/h or m/s) and to memorize the conversion: 1 km/h = 5/18 m/s. Relative speed for same direction is subtraction; opposite direction is addition.

• Distance = Speed x Time; always check units first
• Relative speed (opposite): S1 + S2; same direction: |S1 - S2|
• Boat upstream speed = B - R; downstream = B + R; still water speed = (upstream + downstream)/2
• Average speed for equal distances = 2xy/(x+y), NOT simple average
• Train crossing: time = (length of train + length of object) / relative speed

Time and Work

Time-work problems test how quickly individuals or groups finish a task. The unitary method is the safest approach: convert everything to work done per day. Pipes and cisterns follow the same logic with filling (positive) and leaking (negative).

• If A finishes in n days, A's 1 day work = 1/n
• Combined 1 day work of A and B = 1/A + 1/B; Time = AB/(A+B)
• If A is twice as fast as B, ratio of time = 1:2
• Pipe fills in x hours, leak empties in y hours; net = 1/x - 1/y per hour
• Work equivalence: M1 x D1 x H1 = M2 x D2 x H2 (men x days x hours)

• Using simple average instead of harmonic mean for average speed when distances are equal — always use 2xy/(x+y).
• Calculating profit/loss percentage on SP instead of CP — the denominator for profit% is always CP.
• Adding successive percentage changes directly (e.g., 20% + 10% = 30%) instead of using the a + b + ab/100 formula.
• Ignoring units in TSD — mixing km/h with metres and seconds without converting leads to wrong answers under time pressure.
• In work problems, treating 'A is 3 times as efficient as B' as A takes 3 times longer — it is the opposite: A takes 1/3 the time.

• PCIST mnemonic for word problem types: Percentage, CI/SI, mixtures (alligation), Speed-distance, Time-work — cover these 5 and you cover 80% of Quant.
• Alligation cross: draw an X, put cheaper on top-left, dearer on top-right, mean in the centre, then subtract diagonally. The bottom values are the mixing ratio.
• For CI-SI difference: think of it as the interest on the first year's interest — P x (R/100)^2 for 2 years, easy to visualise.
• Boat problems: think of the boat as a swimmer in a river. Downstream = going with the current (fast, add), Upstream = fighting the current (slow, subtract). Average the two to find still water speed.

• Phase 1 of RBI Grade B has 30 Quant questions in 25 minutes — that is under 50 seconds per question. Do not set up full algebraic equations; use approximation and formula shortcuts for arithmetic problems.
• DI sets in RBI Grade B frequently embed percentage change, ratio, and profit-loss inside table or bar chart questions. Practise recognising the formula type within 10 seconds of reading the question.
• The exam favours 2-step problems: a ratio question may also require a percentage calculation. Always read to the end of the question before starting to solve.
• Avoid long calculations for CI: memorise CI for common values (10% for 2 years = 21%, for 3 years = 33.1%) to quickly verify options.
• In RBI Grade B 2023-24 papers, mixture and alligation, time-work, and TSD appeared with moderate difficulty — these are scoring if done with the standard shortcuts rather than first-principles algebra.