Chapter 5 of 12

42%

IBPS PO Quantitative Aptitude & DI★ Prelims: 5–8 marks direct · Mains: 5–8 (direct + inside caselets) — plus the hidden math in most DI

Arithmetic — Percentage, Profit & Loss, Interest

The engine room of bank quant — 5–8 direct marks plus the hidden math inside every caselet and DI set. One toolkit (percentage as a fraction, the multiplying factor, and the SI/CI relationship) powers percentage, profit-loss, discount, interest and partnership alike. Learn the templates once and a whole family of questions collapses into one-liners.

⏱ 24 min readMedium difficulty✓ Free · exam-pattern aligned

Timed practiceMCQs from this chapter with instant scoring

FlashcardsFormulas & traps on spaced repetition

IBPS PO PYQsSolved previous-year questions

By the end of this chapter you'll be able to…

1Convert percentages to fractions and use the multiplying factor to reach final values in one step
2Apply the successive-change formula to prices, discounts and growth
3Keep the correct base — CP for profit/loss, MP for discount, principal for interest
4Use the CI−SI two-year and three-year shortcuts
5Split profit by the capital×time ratio in partnership
6Recognise the reusable templates: % more/less, consumption–price, successive discount

💡

Why this chapter matters in IBPS PO

Arithmetic word problems are the engine room of bank quant: 5–8 direct marks a paper and the underlying math of nearly every caselet, DI comparison and mixture question. One toolkit — percentage as a fraction, the multiplying factor, and the SI/CI relationship — powers percentage, profit-loss, discount, interest and partnership together, so mastering it lifts the whole section at once. IBPS numbers are engineered for the fraction route, which turns 90-second calculations into one-liners under the sectional clock.

Before you start — revise these

🔗

Simplification & Approximation

The fraction table and fast multiplication that make every template a one-liner.

🔗

Ratio, Proportion, Ages & Partnership

Ratio thinking (25% ⇒ 4:5) is faster than formula-plugging throughout.

Arithmetic — Percentage, Profit & Loss, Interest — IBPS PO Quant

Arithmetic word problems are the language the rest of bank quant speaks. Directly they're 5–8 marks a paper; indirectly they're inside almost every caselet, every DI comparison and every mixture question. And they all run on one toolkit: convert percentages to fractions, use the multiplying factor to reach the final value in one step, and know how simple and compound interest relate. Master that, and percentage, profit-loss, discount and interest stop being separate chapters and become one set of templates.

1. What IBPS actually asks

Directly: 5–8 questions split across percentage, profit-loss-discount, simple & compound interest, and partnership, plus their appearance inside caselet DI. The bank flavour leans on relationships ("SP is 20% above CP, a 10% discount is given…") and clean numbers engineered for the fraction route.

2. The percentage core (everything builds on this)

$x % = \frac{x}{100}$ , and the single biggest speed unlock is converting percentages to fractions before calculating: 12.5% = ⅛, 16.67% = ⅙, 37.5% = ⅜, 62.5% = ⅝.

The multiplying factor (MF): every percentage change is one multiplication.

+20% → ×1.20 (or ×6/5); −25% → ×0.75 (or ×3/4). Never compute "the change" and add it back — go straight to the final value.

Successive change: two changes $a %$ then $b %$ net to $a + b + \frac{ab}{100}$ (signs matter). +20% then −20% = −4%, never zero.

$final = initial \times (1 \pm r /100), net % = a + b + \frac{ab}{100}$

3. Profit, loss & discount (percentage on prices)

All of it is percentage applied to Cost Price (CP), Selling Price (SP), Marked Price (MP):

Profit% $= \frac{S P - C P}{C P} \times 100$ ; Loss% on CP likewise. The base is always CP for profit/loss.
SP from CP: $S P = C P \times (1 + profit %/100)$ — the multiplying factor again.
Discount is on MP: $S P = M P \times (1 - disc %/100)$ .
The MP–CP chain: goods marked $x %$ above cost, then $y %$ discount ⇒ net profit% $= x - y - \frac{x y}{100}$ (same successive-change formula).

Key traps: profit% is on CP but discount% is on MP — never mix bases. And "20% profit" as a fraction is 1/5 of CP, so CP : SP = 5 : 6; ratio thinking beats formula-plugging.

4. Simple vs compound interest (interest = percentage over time)

$S I = \frac{P \cdot R \cdot T}{100}, A = P (1 + \frac{R}{100})^{T}$

SI is linear: the same interest every year. CI compounds: interest on interest.
The gap for 2 years: $C I - S I = P (\frac{R}{100})^{2}$ — a one-line result IBPS asks constantly. For 3 years, $C I - S I = P \cdot \frac{R ^{2}}{10 0 ^{2}} \cdot (3 + \frac{R}{100})$ .
CI as growth: compound interest is population-growth math — $A = P (1 + r /100)^{T}$ is the same multiplying factor chained $T$ times.
Half-yearly compounding: rate → $R /2$ , time → $2 T$ .

Ratio shortcut: at $R %$ , the CI amounts over years form a GP with ratio $(1 + R /100)$ ; and SI makes equal yearly additions — spotting which one applies saves the whole calculation.

5. Partnership (ratio of capital × time)

Profit is shared in the ratio of each partner's capital × months invested:

$share ratio = C_{1} T_{1} : C_{2} T_{2} : \dots$

If A invests ₹12,000 for 12 months and B ₹18,000 for 8 months, ratio $= 12 \times 12 : 18 \times 8 = 144 : 144 = 1 : 1$ . "Working vs sleeping partner" and salary-before-split are just adjustments on top of this ratio.

6. The templates IBPS reuses

Consumption–price: price + $r %$ with fixed spend ⇒ consumption − $\frac{r}{100 + r} \times 100%$ . (25% up ⇒ 20% down.)
% more ↔ % less: A is $x %$ more than B ⇒ B is $\frac{x}{100 + x} \times 100%$ less than A. Convert to a fraction and flip.
Two successive discounts: $d_{1}$ then $d_{2}$ = $d_{1} + d_{2} - \frac{d _{1} d _{2}}{100}$ single equivalent discount.
Exam/marks and mixtures reuse the same percentage-gap logic.

Solved examples

Question 1 of 6

Q1 (profit as ratio). A article is sold at a 25% profit for ₹500. The cost price is?

Show explanation

Solution. 25% profit ⇒ CP:SP = 4:5. SP = ₹500 ⇒ CP = 500 × 4/5 = ₹400.

Question 2 of 6

Q2 (marked-up then discounted). Goods marked 40% above cost are sold at a 25% discount. Net profit%?

Show explanation

Solution. Net = 40 − 25 − (40×25)/100 = 15 − 10 = +5%.

Question 3 of 6

Q3 (CI − SI, 2 years). The difference between CI and SI on ₹8,000 at 10% for 2 years is?

Show explanation

Solution. $P (R /100)^{2} = 8000 \times (1/10)^{2} = 8000/100 =$ ₹80.

Question 4 of 6

Q4 (successive discount). Two successive discounts of 20% and 10% equal a single discount of?

Show explanation

Solution. 20 + 10 − (20×10)/100 = 30 − 2 = 28%.

Question 5 of 6

Q5 (partnership). A puts ₹15,000 for 8 months, B ₹12,000 for 10 months. B's share of ₹9,600 profit?

Show explanation

Solution. Ratio = 15×8 : 12×10 = 120 : 120 = 1:1 ⇒ B gets ₹4,800.

Question 6 of 6

Q6 (consumption–price). Sugar price rises 25%; by what % must a family cut use to keep spend unchanged?

Show explanation

Solution. $\frac{25}{125} \times 100 =$ 20% (25% = ¼ up ⇒ ⅕ down).

8. The protocol

For every arithmetic question:

Convert every percentage to a fraction as you read.
Identify the base — CP for profit/loss, MP for discount, principal for interest.
Reach for the multiplying factor to jump to the final value in one step.
Match to a template (successive change, % more/less, consumption–price, CI−SI, partnership ratio).
Use ratios over formulas when the percentage is a clean fraction (25% ⇒ 4:5).
If the arithmetic turns ugly, you picked the wrong base — re-read "per cent of what".

Key formulas & results

Everything to memorise for the exam hall, in one card. Screenshot this for revision.

Multiplying factor

+r% → ×(1+r/100); −r% → ×(1−r/100)

Go straight to the final value; never add the change separately.

Successive change

net% = a + b + ab/100 (signs matter)

Also = single equivalent for mark-up+discount and two discounts.

Profit/Loss

Profit% = (SP−CP)/CP × 100; SP = CP(1+p/100)

Base is ALWAYS CP for profit/loss.

Discount

SP = MP(1 − d/100)

Discount base is MP, not CP — never mix the two.

Simple interest

SI = P·R·T/100

Linear — equal interest each year.

Compound interest

A = P(1+R/100)^T

Half-yearly: R→R/2, T→2T.

CI − SI (2 yr)

CI − SI = P(R/100)²

3 yr: P·(R²/100²)·(3 + R/100).

Partnership

share ratio = C₁T₁ : C₂T₂ : …

Capital × months invested.

% more ↔ % less

A is x% more than B ⇒ B is x/(100+x)×100 % less than A

Convert to a fraction and flip.

Consumption–price

price +r% ⇒ consumption −r/(100+r)×100 % (same spend)

25% up ⇒ 20% down.

IBPS PO test series

Ready to be tested on this?

Arithmetic — Percentage, Profit & Loss, Interest shows up in every IBPS PO paper — sit a timed one and find out where you actually stand.

5–8Qs in Prelims

Highpriority

Full IBPS PO mocks, real clock
Quantitative Aptitude & DI-only sectionals & chapter tests
All-India rank + topic-level analysis

Free forever · solver-verified questions

⚠️

Traps IBPS PO sets — and how to dodge them

These are the exact option-traps and misreads that cost marks under negative marking.

WATCH OUT

✗ Taking discount% on CP instead of MP (or profit% on SP instead of CP)

✓ Profit/loss is always on CP; discount is always on MP. Circle the base before computing — mixed bases are the #1 profit-loss error.

WATCH OUT

✗ Assuming +r% then −r% returns to the original

✓ Successive equal up-down nets −r²/100 %, never zero. +20%/−20% = −4%. IBPS keeps '0%/no change' as bait.

WATCH OUT

✗ Computing CI the long way when only CI−SI is asked

✓ For 2 years, CI − SI = P(R/100)² directly — no need to compute either interest fully.

WATCH OUT

✗ Adding two successive discounts (20% + 10% = 30%)

✓ Equivalent single discount = d₁ + d₂ − d₁d₂/100 = 28%, not 30%. The same successive-change formula applies.

WATCH OUT

✗ Plugging formulas when a clean fraction is faster

✓ 25% profit ⇒ CP:SP = 4:5; 20% ⇒ 5:6. Ratio thinking is faster and less error-prone than the percentage formula.

WATCH OUT

✗ Wrong base in % more/less questions

✓ 'A is x% more than B' is measured against B; flip the fraction to get B relative to A. Underline 'than whom'.

Exam-pattern practice

PYQ-style questions with full solutions. Work through them as a readiness check — mark yourself honestly and get your gap report at the end.

Readiness check

Are you exam-ready for Arithmetic — Percentage, Profit & Loss, Interest?

7 problems from this chapter. Try each one, reveal the worked solution, mark yourself honestly — get your gap report at the end.

7 questions~5 min worth ~8 marks in IBPS PO exams

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•One toolkit runs percentage, profit-loss, discount, interest and partnership.
•Convert % to fractions; use the multiplying factor to reach the final value in one step.
•Successive change: a + b + ab/100 — also the mark-up+discount and two-discount rule.
•Base discipline: CP for profit/loss, MP for discount, principal for interest.
•CI − SI (2 yr) = P(R/100)²; half-yearly ⇒ R/2, 2T.
•Partnership share = capital × months ratio.
•% more ↔ % less: convert to a fraction and flip; consumption−price: r/(100+r).
•Clean percentages ⇒ ratios (25% ⇒ 4:5) beat formulas.

IBPS PO question blueprint

How this topic is asked, tier by tier — so you can prep to the pattern.

Typical weightage: Prelims: 5–8 marks (of 30) · Mains: 5–8 marks (of 60) + hidden in caselets

Question style	Marks each	Typical count	What it tests
Percentage / profit-loss / discount	1 each	3–5	Multiplying factor, base discipline, successive change
SI / CI / partnership	1 each	1–3	CI−SI gap, growth compounding, capital×time ratio
Inside caselet DI	1.5 each	2–4	The same arithmetic applied to extracted data

Prep strategy

Week 1: percentage toolkit + profit-loss-discount, 25 questions daily via the fraction route.
Week 2: interest (SI/CI shortcuts) and partnership; add the reusable templates.
Ongoing: every caselet you practise is arithmetic revision — track per-question time under 45 seconds.

Exam-hall strategy

Battle-tested tips from mentors and toppers for this topic under the sectional clock.

Convert every percentage to a fraction on the first read.
Identify the base (CP/MP/principal) before touching the numbers.
Use the multiplying factor and successive-change formula to skip intermediate steps.
Prefer ratios when the percentage is a clean fraction.
If the arithmetic gets ugly, re-check 'per cent of what' — you likely picked the wrong base.

Beyond the exam

Where this skill shows up in the job you're competing for — and in life.

The PO desk

Interest accrual, EMI math, processing-fee discounts and margin calculations are literally this chapter applied all day.

Personal finance

Flat vs reducing interest, successive discounts and effective returns are the exact same math banks and shops use on you.

Reading the economy

Inflation, growth rates and margin reporting are percentage reasoning at national scale.

Where else this topic is tested

Prepare once, score in every exam that asks it.

IBPS Clerk / SBI PO & ClerkVery high — arithmetic + DI is the whole quant backbone

RRB PO & ClerkVery high — heavy arithmetic word problems

SSC CGLHigh — same templates, slightly harder numbers

CAT / XAT (QA)Medium — same concepts at higher difficulty

📝 My notes

Saved on this device — sign in to sync · how this works

0/600

Questions aspirants ask

Pulled from the Q&A community and mentor sessions.

Directly 5–8 questions across percentage, profit-loss, interest and partnership, but the true weight is higher — the same arithmetic drives most caselet DI, mixture and data-sufficiency questions. It's the highest-leverage quant chapter after DI itself.

Lead with fractions and ratios; keep formulas as a fallback. IBPS engineers clean numbers (25% profit ⇒ 4:5), so the ratio route is faster and less error-prone. The formulas matter mainly when numbers aren't clean.

Treat CI as growth: A = P(1+r/100)^T is the multiplying factor chained. When only the CI−SI gap is asked, use P(R/100)² for 2 years directly instead of computing both interests.

Almost always a base error — applying discount% to CP or profit% to SP. Profit/loss is on CP; discount is on MP. Fix the base first and the templates fall into place.

More Quantitative Aptitude & DI chapters

Data Interpretation (Table, Bar, Line, Pie, Caselet)The whole quant section in disguise. 30–50% of every IBPS PO quant paper is DI — and DI is…

Simplification & ApproximationThe fastest, most certain marks in the quant section — 5–10 questions in Prelims that a tr…

Number Series — Missing & Wrong Term3–5 fast, high-accuracy marks in every paper — once you can spot the pattern family in 15 …

Quadratic Equations & InequalitiesThe two-equation "compare x and y" set — 0–5 marks that are pure mechanics. You rarely nee…

Take the next step

IBPS PO Quantitative Aptitude & DI — find a tutor

Pair self-study with a tutor, a live course or a coaching centre.

1-on-1 help

🧑‍🏫

Find a verified tutor

School, college and competitive — online or at home.

Find tutors

Live cohorts

Join a live course

Test series and recorded lessons from top creators.

Browse courses

Classroom

Browse coaching centres

Verified institutes near you for every exam.

Find centres

Arithmetic — Percentage, Profit & Loss, Interest

By the end of this chapter you'll be able to…

Before you start — revise these

Arithmetic — Percentage, Profit & Loss, Interest — IBPS PO Quant

1. What IBPS actually asks

2. The percentage core (everything builds on this)

3. Profit, loss & discount (percentage on prices)

4. Simple vs compound interest (interest = percentage over time)

5. Partnership (ratio of capital × time)

6. The templates IBPS reuses

Solved examples

8. The protocol

Key formulas & results

Traps IBPS PO sets — and how to dodge them

Exam-pattern practice

Are you exam-ready for Arithmetic — Percentage, Profit & Loss, Interest?

5-minute revision

IBPS PO question blueprint

Exam-hall strategy

Beyond the exam