Arithmetic Word Problems Questions for IBPS RRB PO

Time, Speed and Distance

Speed tells you how fast something moves. Distance is how far it goes. Time is how long it takes. The golden triangle connects all three. For trains, boats, and relative motion, you just modify the speed value. Relative speed when two objects move toward each other is sum of speeds; when moving in same direction it is difference of speeds.

• Speed = Distance divided by Time. Keep units consistent — km/hr or m/s.
• To convert km/hr to m/s multiply by 5/18. To convert m/s to km/hr multiply by 18/5.
• For a train crossing a pole or person: Distance = Length of train only.
• For a train crossing a platform or another train: Distance = Sum of both lengths.
• Boat upstream speed = Boat speed minus Current speed. Downstream = Boat speed plus Current speed.
• Average speed for equal distances = 2ab divided by (a plus b), NOT simple average.

Time and Work

Think of work as filling a tank. Each person fills a fraction of the tank per day. Add the fractions to get combined efficiency. The Pipe and Cistern problems are the same concept — inlet pipes fill, outlet pipes drain. Always work with fractions per day (efficiency), not total days directly.

• If A completes work in N days, A's one-day work = 1/N.
• Combined one-day work of A and B = 1/A + 1/B.
• Total days together = 1 divided by (1/A + 1/B) = AB/(A+B).
• If one pipe fills in X hrs and another empties in Y hrs, net rate = 1/X minus 1/Y.
• Work is constant. If workers increase, days decrease proportionally.
• Wages are divided in ratio of their efficiencies (work done), not days worked.

Profit, Loss and Discount

Cost Price (CP) is what you buy at. Selling Price (SP) is what you sell at. Marked Price (MP) is the printed price before discount. Profit or Loss is always calculated on CP, not SP. Discount is always calculated on MP, not CP. Successive discounts are not simply added.

• Profit percent = (SP - CP) / CP x 100.
• Loss percent = (CP - SP) / CP x 100.
• SP = CP x (100 + profit%) / 100.
• Discount = MP - SP. Discount percent = Discount / MP x 100.
• For two successive discounts d1 and d2: Net = 100 - [(100-d1)(100-d2)/100].
• If a shopkeeper cheats on weight: Profit% = (True weight - False weight) / False weight x 100.

Simple and Compound Interest

Simple Interest (SI) is calculated on original principal every year — it stays flat. Compound Interest (CI) is calculated on principal plus accumulated interest — it grows like a snowball. For IBPS RRB PO, you will often be asked to find difference between CI and SI for 2 years, or find rate/time using CI formulas.

• SI = PRT/100 where P = Principal, R = Rate per annum, T = Time in years.
• CI = P x (1 + R/100)^T minus P.
• Difference between CI and SI for 2 years = P x (R/100)^2.
• For half-yearly compounding: Rate becomes R/2, Time becomes 2T.
• For quarterly: Rate R/4, Time 4T.
• If sum doubles at SI in N years, Rate = 100/N percent.

Ratio, Proportion and Mixtures

Ratio is a comparison. Proportion means two ratios are equal. Mixtures (Alligation) let you find the mixing ratio when two things of different values are combined to get a target value. The Alligation cross method is the fastest tool — draw a cross, put the target in center, subtract diagonally.

• If A:B = 3:5 and B:C = 2:7, convert to A:B:C by making B common: A:B:C = 6:10:35.
• In alligation: Ratio of mixing = (Higher value - Mean) : (Mean - Lower value).
• Compound ratio: multiply the ratios. a:b and c:d gives ac:bd.
• In mixture replacement: After removing x litres from V litres n times, remaining original = V x (1 - x/V)^n.
• Partnership profits divide in ratio of capital x time.

• Using simple average instead of harmonic mean for average speed when same distance is covered at two different speeds. Always use 2ab/(a+b).
• Calculating discount percent on CP instead of MP. Remember: Profit/Loss on CP, Discount on MP — always.
• Forgetting to adjust rate and time when CI is compounded half-yearly or quarterly. Many candidates apply annual formula directly.
• In Time and Work, dividing wages in ratio of days instead of ratio of efficiency (work done per day). Faster worker earns more per day.
• Adding successive discounts directly (e.g., saying 10% + 5% = 15% discount) instead of applying them one after another. Net is always less than the sum.

• TSD Triangle: Draw a triangle with D on top, S and T at bottom. Cover what you want: cover D = SxT, cover S = D/T, cover T = D/S.
• MPCP Rule: Marked Price minus discount = SP. CP plus profit = SP. Always remember which base each percentage uses: MP for discount, CP for profit.
• CI-SI Trick for 2 years: The difference is just P times (R/100) squared. No need to calculate full CI. Remember it as the interest on first year interest.
• Alligation Cross: Write higher value top-left, lower value top-right, mean in center. Subtract diagonally (cross lines). Result is the mixing ratio. Looks like an X — call it the X-method.

• IBPS RRB PO Prelims has 40 Quant questions in 45 minutes. Arithmetic word problems take 1.5 to 2 minutes each. Target 8-10 correct out of 10-12 such questions. Do not spend more than 2 minutes on any single question.
• In Mains, caselet DI often embeds arithmetic problems — a passage gives data about a shopkeeper or a pipeline and asks 5 questions using profit-loss, ratio, and interest concepts together. Practice reading such passages fast.
• SI and CI questions in recent RRB PO papers frequently ask for the principal or rate when difference between CI and SI is given. Master the shortcut P(R/100)^2 to solve these in under 30 seconds.
• Train and boat problems almost always appear in Prelims. The two most common traps are forgetting to add platform length and confusing upstream-downstream. Solve at least 20 PYQs on each.
• Alligation is a hidden weapon — it can solve mixture questions, average salary questions, and even partnership questions in under 60 seconds. If an Arithmetic question looks complex, check if Alligation applies before trying algebra.