MathsICSE Class 8 · Chapter 7

Percentage, Profit and Loss, Discount and Tax ICSE Class 8: Solved Problems

Updated 15 October 2026 · Fact-checked

In ICSE Class 8, cost price includes overhead expenses such as repairs and transport; profit or loss per cent is always worked out on the cost price; a discount is a percentage of the marked price; and tax such as GST is added as a percentage of the price after discount.

What Percentage, Profit and Loss, Discount and Tax is about

Per cent means "per hundred": $15% = \frac{15}{100}$ . Almost every shopping calculation uses it.

The CISCE Class VIII curriculum asks for slightly advanced problems on:

percentages (increase, decrease, finding the whole from a part),
profit and loss, including overhead expenses (repairs, transport, packing) that are added to the cost price,
discount on the marked (list) price,
tax (sales tax or GST) added to the selling price.

The key words:

Cost price (CP): what the seller pays in total, including overheads.
Selling price (SP): what the seller receives.
Marked price (MP): the price on the label, before discount.
Discount: the reduction on MP. SP $=$ MP $-$ discount.
Tax: added on top of SP; the buyer pays it, and the seller passes it to the government.

Two rules prevent most errors: profit and loss per cent are on CP, and discount per cent is on MP.

Weightage: CISCE publishes no question paper, marking scheme or chapter weightage for Class VIII Mathematics: your school sets and marks the exam. Percentage, Profit and Loss, Discount and Tax sits in the Ratio and Proportion theme of the CISCE Curriculum for Upper Primary Classes (VI-VIII).Source: CISCE Curriculum for Upper Primary Classes (VI-VIII), RDCD 2016

Key concepts

Percentage increase and decrease

To increase a quantity by $r %$ , multiply by $\frac{100 + r}{100}$ . To decrease it by $r %$ , multiply by $\frac{100 - r}{100}$ .

Percentage change $= \frac{change}{original} \times 100$ . Always divide by the original value, not the new one.

To find the whole from a part: if $x %$ of a number is $p$ , the number is $\frac{p \times 100}{x}$ .

Worked example

The price of a book is ₹250. It goes up by 12%. Find the new price.

Try it first, then show the solutionSolution

Multiplier $= \frac{112}{100}$ .
New price $= 250 \times \frac{112}{100} = 280$ .

Answer: ₹280

Profit and loss with overhead expenses

Overhead expenses are extra costs before selling: transport, repairs, packing, labour. They are part of the cost:
$CP = buying price + overheads$ .

Then:

Profit $=$ SP $-$ CP (when SP > CP); Loss $=$ CP $-$ SP (when CP > SP).
Profit % $= \frac{profit}{CP} \times 100$ ; Loss % $= \frac{loss}{CP} \times 100$ .

Worked example

Ravi buys an old cycle for ₹3,600, spends ₹400 on repairs and sells it for ₹4,500. Find his profit per cent.

Try it first, then show the solutionSolution

CP $= 3600 + 400 = ₹4000$ .
Profit $= 4500 - 4000 = ₹500$ .
Profit % $= \frac{500}{4000} \times 100 = 12.5%$ .

Answer: 12.5%

Finding SP or CP from a percentage

With profit $P %$ : $SP = CP \times \frac{100 + P}{100}$ .
With loss $L %$ : $SP = CP \times \frac{100 - L}{100}$ .

To go back from SP to CP, divide by the same factor: $CP = SP \times \frac{100}{100 + P}$ or $SP \times \frac{100}{100 - L}$ .

A common trap: a 5% loss on ₹1,140 is not the same as finding CP. If SP is ₹1,140 after a 5% loss, then SP is 95% of CP.

Worked example

A table is sold for ₹1,140 at a loss of 5%. Find its cost price.

Try it first, then show the solutionSolution

SP is $95%$ of CP.
CP $= 1140 \times \frac{100}{95} = ₹1200$ .
Check: 5% of 1200 is 60, and $1200 - 60 = 1140$ ✓.

Answer: ₹1,200

Discount on the marked price

A discount is a reduction on the marked price (MP), given as a percentage of MP:

Discount $= \frac{rate}{100} \times MP$ .
SP $=$ MP $-$ discount $=$ MP $\times \frac{100 - rate}{100}$ .
Discount % $= \frac{discount}{MP} \times 100$ .

Successive discounts (say 20% then 10%) are applied one after the other; the second is on the already reduced price. So 20% then 10% is not 30%.

Worked example

A jacket is marked ₹1,200 and sold at a 15% discount. Find the selling price.

Try it first, then show the solutionSolution

Discount $= \frac{15}{100} \times 1200 = ₹180$ .
SP $= 1200 - 180 = ₹1020$ .

Answer: ₹1,020

Marking up and giving a discount

Shopkeepers mark goods above the cost price and then give a discount. Their profit depends on both:

1. MP from CP: MP $=$ CP $\times \frac{100 + markup}{100}$ .
2. SP from MP: SP $=$ MP $\times \frac{100 - discount}{100}$ .
3. Profit % is then worked out on CP.

Taking CP $= ₹100$ is a quick way to find the overall percentage.

Worked example

A shopkeeper marks goods 25% above cost price and allows a 10% discount. Find his profit per cent.

Try it first, then show the solutionSolution

Let CP $= ₹100$ . MP $= ₹125$ .
SP $= 125 \times \frac{90}{100} = ₹112.50$ .
Profit $= ₹12.50$ on ₹100, so 12.5%.

Answer: 12.5%

Sales tax and GST

Tax is charged as a percentage of the selling price (the price after any discount) and added to it:

Tax $= \frac{rate}{100} \times SP$ .
Bill amount $=$ SP $+$ tax $=$ SP $\times \frac{100 + rate}{100}$ .

In India this tax is the Goods and Services Tax (GST); rates differ between goods, so questions always tell you the rate.

The tax goes to the government, so it is not part of the seller's profit.

To find the price before tax from a bill: price $=$ bill $\times \frac{100}{100 + rate}$ .

Worked example

A bill including 18% tax is ₹1,180. Find the price before tax.

Try it first, then show the solutionSolution

Bill is $118%$ of the price.
Price $= 1180 \times \frac{100}{118} = ₹1000$ .

Answer: ₹1,000 (tax ₹180)

Maths in real life: Percentage, Profit and Loss, Discount and Tax

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

Suppose a pair of shoes marked ₹1,500 has a "30% off" sticker.

How much do you pay?

Try it first, then show the solutionSolution

Discount $= 30%$ of 1500 $= ₹450$ .
Price $= 1500 - 450 = ₹1050$ .

Answer: ₹1,050

Memory hook: Percent off is a percentage of the marked price.

Adding tax

Imagine a restaurant bill comes to ₹640 before tax, and 5% GST is added.

What is the final bill?

Try it first, then show the solutionSolution

Tax $= 5%$ of 640 $= ₹32$ .
Final bill $= 640 + 32 = ₹672$ .

Answer: ₹672

Memory hook: Tax is added on top of the price.

Overheads and profit

Suppose you buy a used cycle for ₹2,000, fit new tyres for ₹250, and sell it for ₹2,700.

What is your profit per cent?

Try it first, then show the solutionSolution

CP $= 2000 + 250 = ₹2250$ ; profit $= 2700 - 2250 = ₹450$ .
Profit % $= \frac{450}{2250} \times 100 = 20%$ .

Answer: 20%

Memory hook: Money spent before selling is part of the cost.

Topics in this chapter

Percentage, Profit and Loss, Discount and Tax formula sheet

Cost price: $CP = purchase price + overheads$; Repairs, transport and similar costs count.
Profit per cent: $Profit % = \frac{SP - CP}{CP} \times 100$; Always on CP.
SP from CP: $SP = CP \times \frac{100 + P}{100}$; Use 100 − L for a loss.
Selling price after discount: $SP = MP \times \frac{100 - d}{100}$; d = discount per cent, on MP.
Bill with tax: $Bill = SP \times \frac{100 + t}{100}$; t = tax per cent, on SP.
Successive discounts: $SP = MP \times \frac{100 - a}{100} \times \frac{100 - b}{100}$; Not MP × (100 − a − b)/100.

How the school exam asks Percentage, Profit and Loss, Discount and Tax

The question patterns to expect, and the method that works for each.

Question type	How it is asked	Method
Overhead expenses	An article is bought, repaired and transported, then sold. Find the profit or loss per cent.	Add overheads to CP first, then use profit % on CP.
Reverse problems	Sold at ₹1,710 with a 5% loss. At what price should it be sold to gain 5%?	Find CP from the given SP, then the new SP from CP.
Discount	Find the discount per cent, the marked price or the selling price.	Discount is always a percentage of MP.
Mark-up with discount	Marked 40% above CP, discount 15%: find the profit per cent; or find how far above CP to mark.	Take CP = 100 and follow the chain CP → MP → SP.
Tax bills	Find the amount a customer pays after a discount and GST, or the price before tax.	Discount first, then tax on the reduced price.

Tricks to remember Percentage, Profit and Loss, Discount and Tax

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

CP for profit, MP for discount
Profit and loss look at what the seller paid (CP). Discount looks at the label (MP).
Use it when: Choosing the right base for every percentage.
Discount first, tax last
Like a real bill: knock the discount off, then add the tax on what is left.
Use it when: Discount-and-tax questions.
Take 100
When no amounts are given, let CP = ₹100 and follow the percentages.
Use it when: Mark-up and successive-discount questions.
Overheads are cost
Any money spent before the sale goes into CP.
Use it when: Repair and transport questions.

Percentage, Profit and Loss, Discount and Tax: exam-level solved questions

Ordered from exam level to HOTS. Cover the solution, write your own, then compare step by step.

Example 1: Percentage change · 1 mark · MCQExam level

A number increases from 40 to 50. The percentage increase is:
(a) 10%
(b) 20%
(c) 25%
(d) 50%

Try it first, then show the solutionSolution

Change $= 10$ ; original $= 40$ .
$\frac{10}{40} \times 100 = 25%$ .

Answer: (c)

Example 2: Overhead expenses · 3 marks · Short answerExam level

A dealer buys a television for ₹18,000 and spends ₹2,000 on transport. He sells it for ₹22,500. Find his profit per cent.

Try it first, then show the solutionSolution

CP $= 18000 + 2000 = ₹20000$ .
Profit $= 22500 - 20000 = ₹2500$ .
Profit % $= \frac{2500}{20000} \times 100 = 12.5%$ .

Answer: 12.5%

Example 3: Discount · 3 marks · Short answerExam level

The marked price of a mixer is ₹2,400. It is sold at a discount of 12.5%. Find the discount and the selling price.

Try it first, then show the solutionSolution

Discount $= \frac{12.5}{100} \times 2400 = ₹300$ .
SP $= 2400 - 300 = ₹2100$ .

Answer: Discount ₹300; SP ₹2,100

Example 4: Loss to gain · 3 marks · Short answerHarder exam level

By selling a watch for ₹1,710, a shopkeeper loses 5%. At what price should he sell it to gain 5%?

Try it first, then show the solutionSolution

SP is 95% of CP, so CP $= 1710 \times \frac{100}{95} = ₹1800$ .
For a 5% gain: SP $= 1800 \times \frac{105}{100} = ₹1890$ .

Answer: ₹1,890

Example 5: Successive discounts · 4 marks · Long answerHarder exam level

A shop gives successive discounts of 20% and 10% on an article marked ₹5,000. Find the selling price and the single discount that is equivalent to the two.

Try it first, then show the solutionSolution

After 20%: $5000 \times \frac{80}{100} = ₹4000$ .
After a further 10%: $4000 \times \frac{90}{100} = ₹3600$ .
Total discount $= 5000 - 3600 = ₹1400$ .
Single equivalent discount $= \frac{1400}{5000} \times 100 = 28%$ (not 30%).

Answer: SP ₹3,600; equivalent single discount 28%

Example 6: Discount then GST · 4 marks · Long answerHarder exam level

A refrigerator is marked ₹15,000. The shop gives a 10% discount, and then 18% GST is charged. How much does the customer pay?

Try it first, then show the solutionSolution

Discount $= 10%$ of 15000 $= ₹1500$ ; SP $= ₹13500$ .
GST $= 18%$ of 13500 $= ₹2430$ .
Amount paid $= 13500 + 2430 = ₹15930$ .
Check: $15000 \times 0.9 \times 1.18 = 15930$ ✓.

Answer: ₹15,930

Example 7: The full chain · 5 marks · Long answerHOTS / competency

A trader buys an article for ₹2,000 and spends ₹400 on packing and transport. He marks it 25% above his total cost and allows a 10% discount. Tax at 5% is charged on the selling price. Find (i) the marked price (ii) the selling price (iii) the amount the customer pays (iv) the trader's profit per cent.

Try it first, then show the solutionSolution

Total cost $= 2000 + 400 = ₹2400$ .
(i) MP $= 2400 \times \frac{125}{100} = ₹3000$ .
(ii) SP $= 3000 \times \frac{90}{100} = ₹2700$ .
(iii) Customer pays $2700 \times \frac{105}{100} = ₹2835$ .
(iv) Profit $= 2700 - 2400 = ₹300$ (the tax goes to the government); profit % $= \frac{300}{2400} \times 100 = 12.5%$ .

Answer: (i) ₹3,000 (ii) ₹2,700 (iii) ₹2,835 (iv) 12.5%

Case-study practice (Section B style)

Read the situation, then answer every part. In a school exam set on the board pattern this is a 10-mark question split into 3 + 3 + 4 marks.

A festival sale

Suppose a shop pays ₹31,000 for a laptop and spends ₹1,000 on delivery and set-up. The laptop's marked price is ₹40,000. During a festival sale the shop gives a 15% discount, and 18% GST is charged on the discounted price.

(i) · 3 marks
Find the selling price before tax.
Answer
Answer: ₹34,000
Discount $= 15%$ of 40000 $= ₹6000$ . SP $= 40000 - 6000 = ₹34000$ .
(ii) · 3 marks
How much does the customer pay in all?
Answer
Answer: ₹40,120
GST $= 18%$ of 34000 $= ₹6120$ . Total $= 34000 + 6120 = ₹40120$ .
(iii) · 4 marks
Find the shop's profit per cent. Explain why the GST is not included.
Answer
Answer: 6.25%
CP $= 31000 + 1000 = ₹32000$ . Profit $= 34000 - 32000 = ₹2000$ ; profit % $= \frac{2000}{32000} \times 100 = 6.25%$ . The GST is collected from the customer and paid to the government, so it is not the shop's income.

Where the marks are

How a typical answer is split into step marks. Show every step: a right final answer alone rarely earns full marks.

Asha buys an old scooter for ₹12,000, spends ₹1,500 on repairs and sells it for ₹14,850. Find her profit per cent. (3 marks)

Step	Marks
CP $= 12000 + 1500 = ₹13500$	1
Profit $= 14850 - 13500 = ₹1350$	1
Profit % $= \frac{1350}{13500} \times 100 = 10%$	1

A shirt marked ₹800 is sold at a 10% discount, and the shopkeeper still makes a 20% profit. Find the cost price. (4 marks)

Step	Marks
Discount $= 10%$ of 800 $= ₹80$	1
SP $= ₹720$	1
SP is 120% of CP: $CP = 720 \times \frac{100}{120}$	1
CP $= ₹600$	1

An article is marked ₹2,500. A discount of 8% is given and a tax of 10% is charged on the selling price. Find the amount paid. How much less is this than paying the tax on the marked price with no discount? (5 marks)

Step	Marks
Discount $= 8%$ of 2500 $= ₹200$ ; SP $= ₹2300$	1
Tax $= 10%$ of 2300 $= ₹230$	1
Amount paid $= 2300 + 230 = ₹2530$	1
Without discount: $2500 + 250 = ₹2750$	1
Saving $= 2750 - 2530 = ₹220$	1

Where students lose marks in Percentage, Profit and Loss, Discount and Tax

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

Mistake: Leaving overheads out of the cost price
Repairs and transport are money the seller has spent.
Wrong working
CP $= ₹3600$ (repairs ignored)
Right working
CP $= 3600 + 400 = ₹4000$
Do this: List every expense before the sale and add them to CP.
Usually costs: The profit and the percentage.
Mistake: Finding profit per cent on SP
Profit and loss per cent are always on CP.
Wrong working
Profit % $= \frac{500}{4500} \times 100$
Right working
Profit % $= \frac{500}{4000} \times 100 = 12.5%$
Do this: Write 'on CP' next to the formula.
Usually costs: 1 to 2 marks.
Mistake: Adding successive discounts
The second discount is on a smaller price.
Wrong working
20% then 10% = 30% off
Right working
20% then 10% = 28% off
Do this: Apply discounts one at a time.
Usually costs: The final answer.
Mistake: Taking tax on the marked price
Tax is charged on what is actually paid for the goods, after the discount.
Do this: Discount first, then tax on the reduced price.
Usually costs: 1 to 2 marks.
Mistake: Finding CP by subtracting the percentage from SP
If SP is ₹1,140 after a 5% loss, CP is not $1140 + 5%$ of 1140.
Wrong working
CP $= 1140 + 57 = ₹1197$
Right working
CP $= 1140 \times \frac{100}{95} = ₹1200$
Do this: SP is $(100 - L) %$ of CP, so divide.
Usually costs: The whole reverse question.

Practice questions on Percentage, Profit and Loss, Discount and Tax

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 · MCQExam level
15% of 360 is:
(a) 36
(b) 45
(c) 54
(d) 60
Hint
10% is 36; 5% is 18.
Answer
(c)
Q2 · 2 marks · Short answerExam level
An article bought for ₹450 is sold for ₹540. Find the profit per cent.
Hint
Profit on CP.
Answer
Profit $= ₹90$ ; $\frac{90}{450} \times 100 = 20%$ .
Q3 · 2 marks · Short answerExam level
A bag marked ₹850 is sold for ₹782. Find the discount per cent.
Hint
Discount on MP.
Answer
Discount $= ₹68$ ; $\frac{68}{850} \times 100 = 8%$ .
Q4 · 2 marks · Short answerHarder exam level
An article is sold at a loss of 12% for ₹1,320. Find its cost price.
Hint
SP is 88% of CP.
Answer
CP $= 1320 \times \frac{100}{88} = ₹1500$ .
Q5 · 1 mark · Assertion-reasonHarder exam level
Assertion (A): A discount of 20% followed by another 20% is the same as a single discount of 40%.
Reason (R): The second discount is calculated on the reduced price.
(a) (A) is true and (R) is false.
(b) (A) is false and (R) is true.
(c) Both (A) and (R) are true, and (R) is the correct explanation for (A).
(d) Both (A) and (R) are true, but (R) is not the correct explanation for (A).
Hint
Try it on ₹100.
Answer
(b). On ₹100 the price becomes ₹64, a 36% discount, because the second discount is on ₹80.
Q6 · 3 marks · Short answerHarder exam level
The price of rice goes up by 25%. By what per cent must a family cut its consumption so that its spending on rice does not change?
Hint
Spending = price × quantity.
Answer
New price $= 1.25$ times; quantity must become $\frac{1}{1.25} = 0.8$ times, a cut of 20%.
Q7 · 3 marks · Short answerHarder exam level
A trader buys 150 eggs at ₹6 each. 15 eggs break. He sells the rest at ₹8 each. Find his profit per cent.
Hint
CP is for all 150 eggs.
Answer
CP $= 150 \times 6 = ₹900$ . SP $= 135 \times 8 = ₹1080$ . Profit $= ₹180$ ; $\frac{180}{900} \times 100 = 20%$ .
Q8 · 3 marks · Short answerHarder exam level
The price of a phone including 12% GST is ₹2,240. Find the price before tax and the amount of tax.
Hint
The bill is 112% of the price.
Answer
Price $= 2240 \times \frac{100}{112} = ₹2000$ ; tax $= ₹240$ .
Q9 · 4 marks · Long answerHarder exam level
After a discount of 15%, an article sells for ₹1,700, and the shopkeeper makes a profit of 25%. Find the marked price and the cost price.
Hint
SP is 85% of MP and 125% of CP.
Answer
MP $= 1700 \times \frac{100}{85} = ₹2000$ ; CP $= 1700 \times \frac{100}{125} = ₹1360$ .
Q10 · 1 mark · Very short answerHarder exam level
A student scores 342 marks out of 450. What percentage is this?
Hint
Marks ÷ total × 100.
Answer
$\frac{342}{450} \times 100 = 76%$ .
Q11 · 4 marks · Long answerHOTS / competency
A dealer gives a 10% discount and still gains 20%. How many per cent above the cost price is the marked price?
Hint
Let CP = 100; SP = 120 = 90% of MP.
Answer
SP $= ₹120$ , so MP $= 120 \times \frac{100}{90} = ₹133 \frac{1}{3}$ . The marked price is $33 \frac{1}{3} %$ above CP.
Q12 · 4 marks · Long answerHOTS / competency
Two bicycles are each sold for ₹1,200. One is sold at a 20% profit and the other at a 20% loss. Find the overall gain or loss per cent.
Hint
Find each CP separately.
Answer
CP₁ $= 1200 \times \frac{100}{120} = ₹1000$ ; CP₂ $= 1200 \times \frac{100}{80} = ₹1500$ . Total CP $= ₹2500$ , total SP $= ₹2400$ . Loss $= ₹100$ , which is 4%.

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.What are overhead expenses?Show answer
Extra costs such as repairs, transport or packing; they are added to the cost price.
2.Profit per cent is calculated on which price?Show answer
The cost price.
3.Discount per cent is calculated on which price?Show answer
The marked price.
4.On which price is GST charged?Show answer
On the selling price after discount.
5.What single discount equals successive discounts of 10% and 10%?Show answer
19%.
6.CP ₹500, profit 20%. Find SP.Show answer
₹600.
7.MP ₹400, discount 25%. Find SP.Show answer
₹300.
8.A price of ₹100 plus 12% tax is how much?Show answer
₹112.

Best order to study it

Revise percentages: increase, decrease, percentage change and finding the whole.
Learn profit and loss with overhead expenses.
Practise reverse problems: CP from SP and a percentage.
Learn discount, successive discounts and mark-up with discount.
Finish with tax bills that combine discount and GST.

Quick revision checklist

The night before the exam: can you do each of these without looking?

Have you added all overheads to CP?
Is your profit or loss per cent on CP?
Is your discount per cent on MP?
Did you apply successive discounts one after the other?
Did you take the discount before adding tax?
Did you leave tax out of the seller's profit?
Did you divide (not subtract) to get CP from SP?

Percentage, Profit and Loss, Discount and Tax: frequently asked questions

Why is profit per cent calculated on the cost price?

Because it measures how much the seller gained compared with what they put in. The cost price is the money invested.

Is a 20% discount followed by a 20% discount the same as 40%?

No. On ₹100, the first discount gives ₹80 and the second takes 20% of ₹80 (₹16), leaving ₹64. That is a 36% discount.

Who keeps the GST collected by a shop?

The government. The shop only collects it from the customer and pays it on, so it is not counted in the shop's profit.

Can a shop give a discount and still make a profit?

Yes, if the marked price is set far enough above the cost price. For example, marking 25% above CP and giving 10% off still gives a 12.5% profit.

What is the difference between marked price and selling price?

The marked price is the label price. The selling price is what the customer actually pays for the goods after the discount (before tax).

Based on: CISCE Curriculum for Upper Primary Classes (VI-VIII), Mathematics (Class VIII); CISCE RDCD: Curriculum Pre-School to Class VIII