MathsCBSE Class 8 · Fractions in Disguise

Profit, Loss, Discount, Tax and Compound Interest for Class 8

Updated 17 October 2026 · Fact-checked

Profit or loss percentage is calculated on the cost price: profit % = (SP - CP)/CP x 100. A discount of d% on the marked price gives SP = MP(1 - d/100). Tax adds a percentage to a price. Without compounding, p invested at rate r for t years gives p(1 + rt); with compounding it gives p(1 + r)^t, where r is the rate as a decimal. Exams ask for reverse problems, successive discounts and the gain from compounding.

Discount comes off the MRP, but profit percentage is measured on the cost price: 270 out of 900 is 30%.

Illustration drawn for QuestionBuddy.

Understand Profit, Loss, Discount, Tax and Compound Interest

Cost, selling price, profit and loss. The cost price (CP) is what the seller pays and the selling price (SP) is what the buyer pays. If $S P > C P$ the seller gains a profit $= S P - C P$ ; if $S P < C P$ the seller has a loss $= C P - S P$ .
$ $profit % = \frac{profit}{C P} \times 100, loss % = \frac{loss}{C P} \times 100.$ $
The chapter stresses that the percentage is taken on the cost price: if a bag costing 500 sells for 750, the profit is 250 which is 50% of the cost; against the selling price it would be 33.33%, but profit percentage answers "how much did I make compared with what I invested?". The difference between sales and the cost of goods sold is the gross profit; after other expenses such as transport, salaries and electricity are deducted, what remains is the net profit.

Reverse problems. Given the percentage and the SP, use a multiplier: $S P = C P \times (1 + profit rate)$ or $C P \times (1 - loss rate)$ , so $C P = S P \div$ the multiplier. A 12% loss with SP of 80 per kg means $C P = 80 \div 0.88$ .

Discount. The marked price (MRP) is the listed price. A discount of $d %$ reduces the price by $d %$ of the MRP, so $S P = M R P \times (1 - \frac{d}{100})$ . A 35% discount on a 1,800 cooker gives $1800 \times 0.65 = 1170$ ; if its cost price was 900 the profit is 270, which is 30% of the cost.

Successive discounts multiply: 20% off and then 10% off is $0.8 \times 0.9 = 0.72$ , a total discount of 28%, not 30%.

Tax. Taxes such as GST (Goods and Services Tax) and income tax are given as percentages. A tax of $t %$ added to a price $P$ gives the bill $P (1 + t /100)$ ; to find the price before tax divide the bill by $(1 + t /100)$ .

Interest. A bank pays interest on money deposited. In a fixed deposit (FD) at $10%$ p.a. ("per annum", per year) on a principal of 6000, interest for a year is 600.

*Without compounding* (interest paid out every year): the principal stays the same, so after $t$ years the total received is $p + p r t = p (1 + r t)$ , where $r$ is the rate as a decimal. For 6000 at $10%$ for 3 years: $6000 \times (1 + 0.1 \times 3) = 7800$ .
*With compounding* (interest added back each year): the amount is multiplied by $(1 + r)$ every year, so after $t$ years it is $p (1 + r)^{t}$ . For the same deposit: $6000 \times 1. 1^{3} = 7986$ .

Compounding gives more: a gain of 33.1% over 3 years against 30% without compounding.

Percentages, fractions and percentage change are on the previous topic page of this chapter.

Profit, Loss, Discount, Tax and Compound Interest: formulas to remember

Profit and loss percent: $profit % = \frac{S P - C P}{C P} \times 100, loss % = \frac{C P - S P}{C P} \times 100$; The base is the cost price.
Selling price from a rate: $S P = C P (1 \pm \frac{p}{100})$; Plus for profit, minus for loss.
Discount: $S P = M R P (1 - \frac{d}{100})$; The discount is a percentage of the marked price.
Tax: $bill = P (1 + \frac{t}{100})$; Divide the bill by this to get the price before tax.
Amount without compounding: $A = p (1 + r t)$; r is the rate as a decimal, t is in years.
Amount with compounding: $A = p (1 + r)^{t}$; Interest earned = A - p.

How to solve Profit, Loss, Discount, Tax and Compound Interest questions

Follow these steps for profit, discount and interest problems.

1Identify which price is the cost price, the marked price and the selling price.
2Convert each percentage to a multiplier (for example profit 20% is 1.2, loss 20% is 0.8, discount 35% is 0.65).
3For a forward problem, multiply; for a reverse problem, divide by the multiplier.
4Compute the profit or loss percentage on the cost price.
5For two articles, find the total cost and total selling price before computing the overall percentage.
6For interest, choose between p(1 + rt) and p(1 + r)^t, write the rate as a decimal, and compute the powers carefully.
7Check the sign and plausibility of the answer.

Profit, Loss, Discount, Tax and Compound Interest in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Discount and profit

Suppose a shop marks a pressure cooker at Rs 1500 and offers a 20% discount. The shop bought the cooker for Rs 1000.

Find the selling price and the shop's profit percentage.

Try it first, then show the solutionSolution

Selling price $= 1500 \times 0.8 = 1200$ .
Profit $= 1200 - 1000 = 200$ , so profit % $= \frac{200}{1000} \times 100 = 20%$ .

Answer: Rs 1200 and a profit of 20%

Memory hook: Discount is on the marked price; profit is on the cost price.

Compounding

Imagine a Rs 12,000 deposit at 10% p.a. for 2 years in a bank that compounds yearly, compared with one that pays the interest out each year.

Find the difference in the amounts received.

Try it first, then show the solutionSolution

Without compounding: $12000 \times (1 + 0.10 \times 2) = 12000 \times 1.2 = 14400$ .
With compounding: $12000 \times 1. 1^{2} = 12000 \times 1.21 = 14520$ .
Difference $= 14520 - 14400 = 120$ .

Answer: Rs 120 more with compounding

Memory hook: In compounding, interest earns interest.

Tricks to remember Profit, Loss, Discount, Tax and Compound Interest

Short memory aids. Say each one aloud once, then use it on a question the same day.

Profit and loss are on cost price
Profit % and loss % always use CP as the base unless the question says otherwise.
Use it when: Choosing the denominator.
Discount is on marked price
SP = MRP times (1 minus discount rate). The cost price is not involved.
Use it when: Discount questions with a cost price given.
Multipliers for everything
Profit 20% -> 1.2, loss 20% -> 0.8, tax 12% -> 1.12. To reverse, divide.
Use it when: Reverse problems.
Compound means power
Compounding gives a power: multiply by (1 + r) each year; simple gives a straight line: 1 + rt.
Use it when: Interest questions.

Profit, Loss, Discount, Tax and Compound Interest: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Profit percentage · 1 mark · MCQBoard level

A shirt bought for Rs 400 is sold for Rs 460. The profit percentage is: (a) 12% (b) 13% (c) 15% (d) 60%

Try it first, then show the solutionSolution

Profit $= 460 - 400 = 60$ .
Profit % $= \frac{60}{400} \times 100 = 15%$ .

Answer: (c) 15%

Example 2: Discount then profit · 2 marks · Short answerBoard level

An item with a marked price of Rs 1500 is sold at a 20% discount. If its cost price was Rs 1000, find the selling price and the profit percentage.

Try it first, then show the solutionSolution

$S P = 1500 \times 0.8 = 1200$ . (1 mark)
Profit $= 200$ and profit % $= \frac{200}{1000} \times 100 = 20%$ . (1 mark)

Answer: SP = Rs 1200; profit 20%

Example 3: Tax on a bill · 3 marks · Short answerHarder board level

The price of an appliance is Rs 2400 and tax of 12% is added. Find the bill. Another bill is Rs 3360 including 12% tax; find the price before tax.

Try it first, then show the solutionSolution

Bill $= 2400 \times 1.12 = 2688$ . (1 mark)
Price before tax $= 3360 \div 1.12$ . (1 mark)
$3360 \div 1.12 = 3000$ . Check: $3000 \times 1.12 = 3360$ . (1 mark)

Answer: Rs 2688; Rs 3000

Example 4: Two articles, equal selling prices · 3 marks · Short answerHarder board level

A trader sells two radios at Rs 2400 each, one at a 20% profit and the other at a 20% loss. Find the overall profit or loss and its percentage.

Try it first, then show the solutionSolution

First: $C P = 2400 \div 1.2 = 2000$ . Second: $C P = 2400 \div 0.8 = 3000$ . (1 mark)
Total $C P = 5000$ ; total $S P = 4800$ ; loss $= 200$ . (1 mark)
Loss % $= \frac{200}{5000} \times 100 = 4%$ . (1 mark)

Answer: A loss of Rs 200, which is 4%

Example 5: Simple versus compound · 4 marks · Long answerHarder board level

Rs 15,000 is deposited at 8% p.a. for 3 years. Find the amount (i) without compounding (ii) with yearly compounding, and the difference.

Try it first, then show the solutionSolution

(i) $15000 \times (1 + 0.08 \times 3) = 15000 \times 1.24 = 18600$ . (1 mark)
(ii) $1.0 8^{3} = 1.259712$ . (1 mark)
$15000 \times 1.259712 = 18895.68$ . (1 mark)
Difference $= 18895.68 - 18600 = 295.68$ . (1 mark)

Answer: Rs 18,600 without compounding; Rs 18,895.68 with compounding; difference Rs 295.68.

Where students lose marks in Profit, Loss, Discount, Tax and Compound Interest

The slips examiners see most often, and what to write instead.

Mistake: Taking profit percentage on the selling price
The base is the cost price.
Wrong working
"CP 500, SP 750: profit 250 / 750 = 33.3%."
Right working
$\frac{250}{500} \times 100 = 50%$ .
Do this: Write CP under the line before dividing.
Usually costs: The answer.
Mistake: Applying the discount to the cost price
The discount is a percentage of the marked price.
Wrong working
"MRP 1500, CP 1000, 20% discount: SP = 1000 x 0.8 = 800."
Right working
$S P = 1500 \times 0.8 = 1200$ .
Do this: Name the three prices before computing.
Usually costs: 2 marks.
Mistake: Adding successive discounts
Each discount applies to the reduced price.
Wrong working
"20% and 10% discount make 30% discount."
Right working
$0.8 \times 0.9 = 0.72$ , a 28% discount.
Do this: Multiply the multipliers.
Usually costs: The final answer.
Mistake: Using p(1 + rt) when interest is compounded
Compounding gives a power of (1 + r).
Wrong working
"25000 for 2 years at 8% with compounding = 25000 x 1.16."
Right working
$25000 \times 1.0 8^{2} = 29160$ .
Do this: Match the formula to the words "with compounding".
Usually costs: 2 marks.

Exam tips

Write CP, MP and SP separately before any calculation.
Convert every percentage to a multiplier; reverse problems become simple divisions.
For two articles, add costs and selling prices to get the overall result.
Write the rate as a decimal in compound interest and show the power expansion.
State "profit" or "loss", the amount, and the percentage clearly.

Practice questions on Profit, Loss, Discount, Tax and Compound Interest

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · Assertion-reasonBoard level
Assertion (A): A 10% rise in price followed by a 10% fall leaves the price unchanged.
Reason (R): 1.1 x 0.9 = 0.99, not 1.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Hint
Multiply the multipliers.
Answer
(d). The net multiplier is $1.1 \times 0.9 = 0.99$ , so the price falls by 1%. A is false; R is true (and shows why A is false).
Q2 · 2 marks · Very short answerBoard level
A pen is bought for Rs 480 and sold for Rs 600. Find the profit and the profit percentage.
Hint
Profit percentage is on the cost price.
Answer
Profit $= 600 - 480 = 120$ ; profit % $= \frac{120}{480} \times 100 = 25%$ .
Q3 · 3 marks · Short answerHarder board level
After a 12% discount, a bicycle is bought for Rs 3300. Find the marked price and the amount of the discount.
Hint
The selling price is 88% of the marked price.
Answer
$M P \times 0.88 = 3300$ , so $M P = 3300 \div 0.88 = 3750$ . Discount $= 3750 - 3300 = 450$ (which is 12% of 3750).
Q4 · 4 marks · Long answerHOTS / competency
A shop offers two successive discounts of 20% and then 10% on an item marked Rs 2000. (i) Find the final price. (ii) Find the single equivalent discount percentage. (iii) A rival shop offers a flat 30%. Which is cheaper, and by how much?
Hint
Apply 0.8 and then 0.9, then compare with 0.7.
Answer
(i) $2000 \times 0.8 = 1600$ , then $1600 \times 0.9 = 1440$ . (ii) Total discount $= 2000 - 1440 = 560$ , which is $\frac{560}{2000} \times 100 = 28%$ . (iii) A flat 30% gives $2000 \times 0.7 = 1400$ . The rival is cheaper by $1440 - 1400 = 40$ rupees.
Q5 · 4 marks · Case-basedHOTS / competency
Case study: Rs 25,000 is placed in a fixed deposit at 8% p.a. for 2 years.
(i) Find the amount if the interest is paid out each year (no compounding). (1 mark)
(ii) Find the amount with yearly compounding. (1 mark)
(iii) How much extra does compounding give? (1 mark)
(iv) Find the percentage gain over the 2 years in each case. (1 mark)
Hint
Without compounding: 25000(1 + 0.08 x 2). With: 25000 x 1.08^2.
Answer
(i) $25000 \times (1 + 0.16) = 29000$ . (ii) $25000 \times 1.0 8^{2} = 25000 \times 1.1664 = 29160$ . (iii) $29160 - 29000 = 160$ rupees. (iv) Without compounding $16%$ ; with compounding $\frac{4160}{25000} \times 100 = 16.64%$ .

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.On what is profit % calculated?Show answer
The cost price.
2.What is SP when a discount of d% is given on MRP?Show answer
MRP x (1 - d/100).
3.What is gross profit?Show answer
Sales minus the cost of the goods sold.
4.What is the amount without compounding?Show answer
p(1 + rt).
5.What is the amount with compounding?Show answer
p(1 + r)^t.
6.What does p.a. mean?Show answer
Per annum, that is, per year.

Profit, Loss, Discount, Tax and Compound Interest: frequently asked questions

Is the net profit the same as the gross profit?

No. Net profit is what remains of the gross profit after other expenses such as transport, salaries and electricity.

Why does compounding give more?

Each year the interest is added to the deposit, so the next year's interest is calculated on a bigger amount.

Is the GST part of the price shown?

The chapter explains that tax is part of the amount you pay and goes to the government; a bill shows the price and the tax separately.

How do I find the interest only?

Subtract the principal from the amount: p x r x t without compounding, and p(1 + r)^t - p with compounding.