Chapter 4 of 7

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Tamil Nadu (TNBSE)Class 8 Mathematics★ 8-12 marks in the TN Class 8 annual exam through MCQs and money, interest and proportion problems

Life Mathematics

Samacheer Kalvi (TN State Board) Class 8 Maths Chapter 4, Life Mathematics. Percentage, profit and loss, discount, simple and compound interest, direct and inverse proportion, and time and work. Notes with formulas, worked examples, common mistakes, book-back practice and quick revision.

⏱ 22 min readMedium difficulty✓ Free · NCERT-aligned

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Study Guide

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Key points, glossary and the questions most likely to show up.

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

1Calculate profit, loss and discount percentages
2Compute simple and compound interest
3Distinguish direct and inverse proportion
4Solve time-and-work problems
5Apply percentage in real situations

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Why this chapter matters

Life Mathematics applies maths to money, interest, proportion and work — skills used every day and tested heavily in the TN Class 8 exam. Compound interest and proportion problems are reliable scorers.

Before you start — revise these

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Class 7 — Comparing quantities

Percentage and ratios.

Life Mathematics — Class 8 Maths (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 8 Mathematics, Chapter 4. Everyday maths — money, interest, proportion and work.

1. About this chapter

This chapter applies maths to daily life: percentage, profit and loss, discount, simple and compound interest, proportion, and time and work.

2. Percentage, profit, loss and discount

Profit% = (Profit / CP) × 100; Loss% = (Loss / CP) × 100 (CP = cost price).
Discount = Marked Price − Selling Price; Discount% = (Discount / MP) × 100.

3. Simple and compound interest

Simple interest: SI = (P × N × R) / 100; Amount = P + SI.
Compound interest: A = P(1 + R/100)ⁿ; CI = A − P (interest on interest).

4. Proportion and work

Direct proportion: as one quantity increases the other increases; x/y = constant.
Inverse proportion: as one increases the other decreases; x × y = constant.
Time and work: if a person does a work in n days, work done in 1 day = 1/n.

5. Worked examples

Example 1. An item bought for ₹400 is sold for ₹500. Find the profit%. Profit = 100; Profit% = (100/400) × 100 = 25%.

Example 2. Find the compound interest on ₹1000 for 2 years at 10% p.a. A = 1000(1 + 10/100)² = 1000(1.1)² = 1210; CI = 1210 − 1000 = ₹210.

Example 3. If 5 workers finish a job in 12 days, how long for 10 workers? (inverse proportion) 5 × 12 = 10 × d → d = 60/10 = 6 days.

6. Common mistakes

Mistake: Taking the percentage on the wrong base. Fix: Profit/loss% is on CP; discount% is on MP.
Mistake: Using the SI formula for compound interest. Fix: CI uses A = P(1 + R/100)ⁿ.
Mistake: Confusing direct and inverse proportion. Fix: Direct: x/y constant; inverse: x × y constant.

7. Practice (book-back style)

An article costing ₹250 is sold for ₹200. Find the loss%.
Find the SI on ₹2000 for 3 years at 5% p.a.
Find the CI on ₹5000 for 2 years at 10% p.a.
If 8 pipes fill a tank in 6 hours, how long for 12 pipes?
A shopkeeper gives 20% discount on an item marked ₹500. Find the selling price.

8. Answer key

Loss = 50; Loss% = (50/250) × 100 = 20%.
SI = (2000 × 3 × 5)/100 = ₹300.
A = 5000(1.1)² = 6050; CI = ₹1050.
8 × 6 = 12 × t → t = 48/12 = 4 hours.
Discount = 20% of 500 = 100; SP = 500 − 100 = ₹400.

9. Quick revision

Chapter 4 · percentage, profit/loss, interest, proportion, work.
Profit% = (profit/CP)×100; Discount% = (discount/MP)×100.
SI = PNR/100; CI: A = P(1 + R/100)ⁿ, CI = A − P.
Direct: x/y constant; Inverse: x × y constant.
Work in 1 day = 1/n.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Profit / loss percent

Profit% = (Profit/CP)×100; Loss% = (Loss/CP)×100

Always on the cost price.

Simple interest

SI = (P × N × R)/100

Amount = P + SI.

Compound interest

A = P(1 + R/100)ⁿ; CI = A − P

Interest on interest.

Proportion

direct: x/y constant; inverse: x×y constant

Choose by how quantities change.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Taking the percentage on the wrong base

✓ Profit/loss% is on CP; discount% is on MP.

WATCH OUT

✗ Using the SI formula for compound interest

✓ CI uses A = P(1 + R/100)ⁿ.

WATCH OUT

✗ Confusing direct and inverse proportion

✓ Direct: x/y constant; inverse: x × y constant.

NCERT exercises (with solutions)

Every NCERT exercise from this chapter — what it covers and how many questions to expect.

Multiple choice questions

MCQs on percentage, interest and proportion.

Questions

Money / interest problems

Profit, loss, discount and interest sums.

Questions

Proportion / work

Direct/inverse proportion and time-and-work.

Questions

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· Numerical

An article costing ₹250 is sold for ₹200. Find the loss%.

▶ Show solution

Loss = 50; Loss% = (50/250)×100 = 20%.

Q2EASY· Numerical

Find the SI on ₹2000 for 3 years at 5% p.a.

▶ Show solution

SI = (2000 × 3 × 5)/100 = ₹300.

Q3MEDIUM· Numerical

Find the CI on ₹5000 for 2 years at 10% p.a.

▶ Show solution

A = 5000(1.1)² = 6050; CI = ₹1050.

Q4MEDIUM· Proportion

If 8 pipes fill a tank in 6 hours, how long for 12 pipes?

▶ Show solution

8 × 6 = 12 × t → t = 4 hours (inverse proportion).

Q5EASY· Numerical

A shopkeeper gives 20% discount on an item marked ₹500. Find the selling price.

▶ Show solution

Discount = 100; SP = 500 − 100 = ₹400.

Q6EASY· Numerical

An item bought for ₹400 is sold for ₹500. Find the profit%.

▶ Show solution

Profit% = (100/400)×100 = 25%.

5-minute revision

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

•Chapter 4 of Samacheer Kalvi Class 8 Mathematics.
•Profit% = (profit/CP)×100; Discount% = (discount/MP)×100.
•SI = PNR/100; CI: A = P(1 + R/100)ⁿ, CI = A − P.
•Direct: x/y constant; Inverse: x × y constant.
•Time-and-work: one day's work = 1/n.
•Choose the right base for each percentage.

Tamil Nadu (TNBSE) marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: 8-12 marks across MCQ, money and proportion problems

Question type	Marks each	Typical count	What it tests
MCQ	1	1-2	Percentage and interest facts
Money / Interest	2-3	1-2	Profit/loss, discount, interest
Proportion / Work	2-3	1	Direct/inverse, time-and-work

Prep strategy

Use CP as the base for profit/loss
Apply the CI formula A = P(1 + R/100)ⁿ
Decide direct vs inverse proportion
Use 1/n for one day's work

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Shopping

Discounts and profit/loss appear in everyday purchases.

Banking

Simple and compound interest govern savings and loans.

Planning

Proportion and time-and-work schedule tasks and resources.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

Identify CP, SP and MP correctly
Use the right interest formula
Set up proportion equations clearly
Show steps for partial marks

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

Find the rate given the compound interest for two years.
Solve a combined time-and-work problem with three workers.

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

TN Class 8 Annual ExamHigh

Foundation / NMMS MathematicsMedium

School unit testsHigh

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Questions students ask

The real ones — pulled from the Q&A community and tutor sessions.

Because compound interest is calculated on the growing amount (principal plus accumulated interest), so each period earns interest on previous interest too.

If both quantities increase or decrease together it is direct (x/y constant); if one increases as the other decreases it is inverse (x × y constant).

Practice more, ask doubts, find a tutor

Tamil Nadu (TNBSE) Class 8 mock tests

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