Arithmetic

About 6 min · Quantitative Aptitude · English

Time worked out from the lesson's 408 words at 150 words a minute, plus a minute for each question.

Arithmetic forms the backbone of the Quantitative Aptitude section in IBPS PO Prelims. Mastery here is non-negotiable—these topics offer quick marks if your fundamentals are solid.

Key ideas

Percentage is a ratio out of 100. Every percentage problem converts to a fraction or decimal for calculation. Know fraction equivalents cold: 25% = 1/4, 33.33% = 1/3, 12.5% = 1/8.
Ratio compares quantities; proportion equates two ratios. When a ratio is given as a : b, actual values are ax and bx where x is the multiplier you must find.
Average = Sum ÷ Count. Weighted average applies when groups have different sizes. The average of an arithmetic progression equals the middle term (or the mean of the two middle terms when the number of terms is even).
Profit and Loss are always calculated on Cost Price (CP). Discount is always on Marked Price (MP). Mixing these up is a common error.
Simple Interest grows linearly; Compound Interest grows exponentially. For 2-year problems, CI − SI = P × (R/100)².

Watch out for

Confusing base for percentage calculations → Profit/Loss is always on CP; Discount is always on MP. Write the formula before substituting.
Adding percentages directly for successive changes → Two successive 10% increases ≠ 20%. Use the formula a + b + ab/100 = 10 + 10 + 1 = 21%.
Forgetting to equalize time in partnership problems → Always convert to same unit (months). A 6-month investment and a 12-month investment are not comparable directly.

Quick reference

Profit % = (SP − CP) / CP × 100 — always on CP
SI = PRT/100; CI − SI (2 yrs) = PR²/10000
Combined work rate = Sum of individual rates
Alligation gives quantity ratio directly via criss-cross
Train problems: Add lengths when crossing another train or platform

Check yourself: 3 questions

1. A shopkeeper marks his goods 40% above the cost price and allows a discount of 20% on the marked price. If he sells an article for Rs. 896, what is his profit percentage?
2. A sum of money amounts to Rs. 13,380 in 2 years and Rs. 14,490 in 3 years at simple interest. What is the rate of interest per annum?
3. Two pipes A and B can fill a tank in 24 minutes and 32 minutes respectively. If both pipes are opened together, after how many minutes should pipe B be closed so that the tank is full in 18 minutes?

This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.

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