MathsICSE Class 8 · Percentage, Profit and Loss, Discount and Tax

Discount, Successive Discounts and Sales Tax: ICSE Class 8 Maths

Updated 17 October 2026 · Fact-checked

Discount $=$ marked price $-$ selling price, and discount percent is on the marked price: $SP = MP\left(1 - \frac{d}{100}\right)$. Successive discounts multiply their factors. A tax of $t\%$ is added on the price on which it is charged: bill $= \text{price} \times \left(1 + \frac{t}{100}\right)$.

Each discount applies to the reduced price, so 20% then 10% is 28% off, not 30%; tax is added last on the discounted price.

Illustration drawn for QuestionBuddy.

Understand Discount, Successive Discount and Sales Tax

The CISCE curriculum includes discount and tax in slightly advanced percentage problems.

Marked price and discount. The marked price (MP) is the price printed on the article. A discount is a reduction on MP: $S P = M P - discount$ . Discount percent is on MP, so $S P = M P \times \frac{100 - d}{100}$ .

Successive discounts. Two discounts of $d_{1} %$ and $d_{2} %$ are applied one after the other, each on the reduced price: $S P = M P \times (1 - \frac{d _{1}}{100}) (1 - \frac{d _{2}}{100})$ . They never add up. A $20%$ discount followed by $10%$ gives $0.8 \times 0.9 = 0.72$ , a single discount of $28%$ , not $30%$ .

Markup and discount. A trader marks the article above cost ( $M P = C P \times (1 + m /100)$ ) and then offers a discount. The profit is $S P - C P$ , always on CP. The combined factor is $(1 + m /100) (1 - d /100)$ .

Sales tax / GST on a bill. A tax of $t %$ on a price is $\frac{t}{100}$ of that price, and the bill is the price plus the tax. The tax is charged on the price actually paid for the item (after discount) unless the question says otherwise. Tax rates in the problems below are assumed values chosen for practice.

Working backwards. If the final bill is known, divide by $(1 + t /100)$ to get the price before tax, then divide by $(1 - d /100)$ to get the marked price. Always undo the steps in reverse order.

Discount, Successive Discount and Sales Tax: formulas to remember

Selling price after discount: $S P = M P \times \frac{100 - d}{100}$; Discount is on the marked price.
Successive discounts: $S P = M P (1 - \frac{d _{1}}{100}) (1 - \frac{d _{2}}{100})$; Multiply the factors.
Bill with tax: $Bill = price \times \frac{100 + t}{100}$; Tax on the price charged.
Markup then discount: $S P = C P (1 + \frac{m}{100}) (1 - \frac{d}{100})$; Profit is SP - CP.

How to solve Discount, Successive Discount and Sales Tax questions

Apply each percentage step in the order given; undo in reverse for working backwards.

1Identify MP, discount percent, and the price on which tax is charged.
2Compute the price after discount.
3Compute the tax on that price and add it for the bill.
4For successive discounts, multiply factors instead of adding percents.
5For reverse problems, undo tax first, then discount.

Discount, Successive Discount and Sales Tax 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.

Festival sale

Suppose a jacket is marked Rs 2,000 and a shop offers 20% off, then a further 10% off the reduced price at the billing counter.

Find the final price and the single equivalent discount.

Try it first, then show the solutionSolution

After first discount: $2000 \times 0.8 = 1600$ .
After second: $1600 \times 0.9 = 1440$ . Single discount $= \frac{560}{2000} \times 100 = 28%$ .

Answer: Rs 1,440; 28% single equivalent.

Memory hook: Successive discounts multiply, never add.

Tricks to remember Discount, Successive Discount and Sales Tax

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

Factor method
Write each percent as a factor (0.8, 0.9, 1.05) and multiply them.
Use it when: Chains of discounts and taxes.
Undo in reverse
To find the marked price, divide out tax first, then discount.
Use it when: Working backwards.

Discount, Successive Discount and Sales Tax: solved examples

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

Example 1: Selling price after discount · 1 mark · MCQBoard level

An article marked Rs 800 is sold at a 25% discount. The selling price is:
(a) Rs 200 (b) Rs 600 (c) Rs 700 (d) Rs 825

Try it first, then show the solutionSolution

Discount $= 200$ ; $S P = 800 - 200 = 600$ .

Answer: (b)

Example 2: Bill with discount and tax · 3 marks · Short answerBoard level

A watch is marked Rs 2,500. A discount of 12% is given and tax of 5% is charged on the discounted price. Find the amount payable.

Try it first, then show the solutionSolution

Discounted price $= 2500 \times 0.88 = 2200$ .
Tax $= 2200 \times 0.05 = 110$ .
Amount payable $= 2200 + 110 = 2310$ .

Answer: Rs 2,310

Example 3: Single equivalent discount · 3 marks · Short answerHarder board level

Find the single discount equivalent to successive discounts of 20% and 10%.

Try it first, then show the solutionSolution

Factor $= 0.8 \times 0.9 = 0.72$ .
Single discount $= 1 - 0.72 = 0.28 = 28%$ .
Not $30%$ , because the second discount is on the reduced price.

Answer: 28%

Example 4: Markup then discount · 4 marks · Short answerHarder board level

A dealer marks an article 40% above its cost price of Rs 2,000 and then allows a 15% discount. Find the selling price and the profit percent.

Try it first, then show the solutionSolution

MP $= 2000 \times 1.40 = 2800$ .
SP $= 2800 \times 0.85 = 2380$ .
Profit $= 380$ ; $\frac{380}{2000} \times 100 = 19%$ (also $1.4 \times 0.85 = 1.19$ ).

Answer: SP Rs 2,380; profit 19%

Example 5: Working back from the bill · 4 marks · Long answerHOTS / competency

A customer paid Rs 1,890 for a bag after a 10% discount on the marked price, with 5% tax charged on the discounted price. Find the marked price and the tax paid.

Try it first, then show the solutionSolution

Price before tax $= 1890 \times \frac{100}{105} = 1800$ .
Tax $= 1890 - 1800 = 90$ .
MP $= 1800 \times \frac{100}{90} = 2000$ .
Check: $2000 \times 0.9 = 1800$ ; $1800 \times 1.05 = 1890$ .

Answer: MP Rs 2,000; tax Rs 90

Where students lose marks in Discount, Successive Discount and Sales Tax

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

Mistake: Adding successive discounts
The second discount is on a reduced price.
Wrong working
$20% + 10% = 30%$ discount.
Right working
$0.8 \times 0.9 = 0.72$ ; discount $28%$ .
Do this: Convert to factors and multiply.
Usually costs: Answer mark.
Mistake: Calculating the discount percent on the selling price
Discount is on MP.
Wrong working
MP $1500$ , SP $1275$ : $\frac{225}{1275} \times 100 \approx 17.6%$ .
Right working
$\frac{225}{1500} \times 100 = 15%$ .
Do this: MP is always the denominator for discount.
Usually costs: Answer mark.

Exam tips

Write the factor for each step (0.88, 1.05) before multiplying.
Check a reverse problem by going forwards again.
If tax is on the marked price, the question will say so; otherwise use the discounted price.

Practice questions on Discount, Successive Discount and Sales 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 · MCQBoard level
A 20% discount on a marked price of Rs 450 gives a selling price of:
(a) Rs 360 (b) Rs 90 (c) Rs 430 (d) Rs 540
Hint
$450 \times 0.8$ .
Answer
(a)
Q2 · 2 marks · Short answerBoard level
A marked price is Rs 1,500 and the selling price Rs 1,275. Find the discount percent.
Hint
Discount is on MP.
Answer
Discount $= 225$ ; $\frac{225}{1500} \times 100 = 15%$ .
Q3 · 3 marks · Short answerHarder board level
A shirt marked Rs 1,600 is sold after a 25% discount, and a tax of 12% is then added on the discounted price. Find the bill amount.
Hint
Two multiplications.
Answer
$1600 \times 0.75 = 1200$ ; $1200 \times 1.12 = 1344$ . Bill Rs 1,344.
Q4 · 4 marks · Short answerHarder board level
A dealer buys an article for Rs 5,000, marks it up by 30% and allows a 10% discount. Find his profit percent.
Hint
Use 1.3 x 0.9.
Answer
MP $= 6500$ ; SP $= 5850$ ; profit $= 850$ ; $\frac{850}{5000} \times 100 = 17%$ .
Q5 · 4 marks · Long answerHOTS / competency
For a marked price of Rs 4,000, shop P offers successive discounts of 30% and 10%; shop Q offers 25% and 15%. Which shop is cheaper and by how much?
Hint
Compare the multiplying factors.
Answer
P: $4000 \times 0.7 \times 0.9 = 2520$ . Q: $4000 \times 0.75 \times 0.85 = 2550$ . Shop P is cheaper by Rs 30.

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 discount percent calculated?Show answer
The marked price.
2.Single discount equivalent to 20% and 10%?Show answer
28%.
3.Bill with tax t% on price P?Show answer
P x (100 + t)/100.
4.To find MP from a bill, which step first?Show answer
Remove the tax first, then undo the discount.

Discount, Successive Discount and Sales Tax: frequently asked questions

Is GST the same as sales tax in these sums?

For Class 8 practice, both are a percentage added to the price; the rate in each question is stated.

Does discount change cost price?

No; it changes only the selling price.