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

Profit, Loss and Overhead Expenses: ICSE Class 8 Maths Problems

Q: What if the question gives only a percentage and no price?

Take CP = 100 and work with it.

Updated 17 October 2026 · Fact-checked

Effective cost price = purchase price + overhead expenses (repairs, transport, etc.). Profit $= SP - CP$ or loss $= CP - SP$; profit or loss percent is always on the cost price: $\text{gain}\% = \frac{\text{profit}}{CP} \times 100$. Then $SP = CP\left(1 \pm \frac{r}{100}\right)$.

Understand Profit, Loss and Overhead Expenses

The CISCE curriculum asks for slightly advanced percentage, profit and loss problems, including overhead expenses.

Cost price with overheads. Any extra expense spent to buy or prepare an item (carriage, repairs, packing) is added to the purchase price. This total is the effective cost price (CP); profit and loss percentages use it.

Profit and loss. If $S P > C P$ : profit $= S P - C P$ . If $S P < C P$ : loss $= C P - S P$ . Percentages are on CP:
$ $Profit % = \frac{Profit}{C P} \times 100, Loss % = \frac{Loss}{C P} \times 100.$ $

Using a percent to find SP or CP.

$S P = C P \times \frac{100 + p}{100}$ for a gain of $p %$ .
$S P = C P \times \frac{100 - l}{100}$ for a loss of $l %$ .
Reverse: $C P = S P \times \frac{100}{100 + p}$ or $C P = S P \times \frac{100}{100 - l}$ .

Two articles sold at the same price. If one earns $x %$ and the other loses $x %$ , there is always a net loss (because the gain is on a smaller cost). Find each CP separately from its SP, add, and compare with the total SP.

Chain sales. A sells to B at a profit, B sells to C at a profit: the buyer's CP is the previous seller's SP. Work backwards with the reverse formula one step at a time.

Mixed selling. When different portions are sold at different rates, add the revenue from each portion before comparing with the total CP.

Profit, Loss and Overhead Expenses: formulas to remember

Effective cost price: $C P = purchase price + overhead expenses$; Profit and loss use this CP.
Percentage on CP: $Gain% = \frac{S P - C P}{C P} \times 100$; Never on SP.
SP from gain or loss: $S P = C P \times \frac{100 \pm r}{100}$; Plus for gain, minus for loss.
CP from SP: $C P = S P \times \frac{100}{100 \pm r}$; Reverse of the above.

How to solve Profit, Loss and Overhead Expenses questions

First fix the effective CP, then compute profit or loss, then the percentage on that CP.

1Add every overhead to the purchase price to get CP.
2Compare SP with CP: profit or loss.
3Express profit or loss as a percentage of CP.
4When SP and a percent are given, use the reverse formula to find CP.
5For chain or mixed sales, work one step at a time and re-check totals.

Profit, Loss and Overhead Expenses 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.

Repairing before selling

Suppose a second-hand bicycle is bought for Rs 3,200, repaired for Rs 300 and painted for Rs 500, then sold for Rs 4,500.

Find the gain percent.

Try it first, then show the solutionSolution

CP $= 3200 + 300 + 500 = 4000$ .
Profit $= 4500 - 4000 = 500$ ; gain $= \frac{500}{4000} \times 100 = 12.5%$ .

Answer: 12.5%.

Memory hook: Overheads join the cost, not the selling price.

Tricks to remember Profit, Loss and Overhead Expenses

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

Percent is of CP
Profit or loss percentage always has CP in the denominator.
Use it when: Every profit and loss question.
Equal SP, equal x%
One gains x%, one loses x% at the same SP: net loss every time.
Use it when: Two-article questions.

Profit, Loss and Overhead Expenses: solved examples

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

Example 1: Gain percent · 1 mark · MCQBoard level

An article costing Rs 250 is sold for Rs 300. The gain percent is:
(a) 20% (b) 16.67% (c) 50% (d) 25%

Try it first, then show the solutionSolution

Profit $= 50$ ; $\frac{50}{250} \times 100 = 20%$ .

Answer: (a)

Example 2: Effective cost price · 3 marks · Short answerBoard level

Raman buys a refrigerator for Rs 4,800, spends Rs 600 on repairs and Rs 200 on transport, and sells it for Rs 6,300. Find the profit percent.

Try it first, then show the solutionSolution

CP $= 4800 + 600 + 200 = 5600$ .
Profit $= 6300 - 5600 = 700$ .
Gain $= \frac{700}{5600} \times 100 = 12.5%$ .

Answer: 12.5%

Example 3: Finding CP from SP · 3 marks · Short answerHarder board level

A trader sells a bag for Rs 1,036 and earns 12% profit. Find the cost price.

Try it first, then show the solutionSolution

$S P = C P \times \frac{112}{100}$ .
$C P = 1036 \times \frac{100}{112} = 925$ .
Check: $925 + 12% of 925 = 925 + 111 = 1036$ .

Answer: Rs 925

Example 4: Equal selling prices · 4 marks · Short answerHarder board level

Two radios are each sold for Rs 1,200, one at a gain of 20% and the other at a loss of 20%. Find the overall gain or loss percent.

Try it first, then show the solutionSolution

CP of first $= 1200 \times \frac{100}{120} = 1000$ .
CP of second $= 1200 \times \frac{100}{80} = 1500$ .
Total CP $= 2500$ ; total SP $= 2400$ ; loss $= 100$ .
Loss $= \frac{100}{2500} \times 100 = 4%$ .

Answer: Loss of 4%

Example 5: Mixed selling rates · 4 marks · Case-basedHOTS / competency

A grocer buys 40 kg of rice at Rs 25 per kg. He sells 30 kg at Rs 32 per kg and the rest at Rs 20 per kg. (i) Find his gain percent. (ii) At what price per kg must the last 10 kg be sold to make exactly 20% overall?

Try it first, then show the solutionSolution

CP $= 40 \times 25 = 1000$ . SP $= 30 \times 32 + 10 \times 20 = 960 + 200 = 1160$ .
(i) Profit $= 160$ ; gain $= 16%$ .
(ii) Target SP $= 1000 \times 1.20 = 1200$ . Last 10 kg must bring $1200 - 960 = 240$ , i.e. Rs 24 per kg.

Answer: (i) 16%; (ii) Rs 24 per kg

Where students lose marks in Profit, Loss and Overhead Expenses

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

Mistake: Calculating the percentage on the selling price
Profit and loss percentages are on CP.
Wrong working
CP $250$ , SP $300$ : $\frac{50}{300} \times 100 = 16.7%$ .
Right working
$\frac{50}{250} \times 100 = 20%$ .
Do this: Write CP under the fraction bar before dividing.
Usually costs: Answer mark.
Mistake: Leaving out overhead expenses
Repairs and transport raise the cost price.
Wrong working
CP taken as $4800$ : profit $1500$ , gain $31.25%$ .
Right working
CP $= 5600$ ; gain $12.5%$ .
Do this: List all expenses in a column and add.
Usually costs: Most of the marks.

Exam tips

List every expense in a column; the CP line earns a method mark.
Say "gain on CP" in your working.
In a two-article question never assume zero net profit.

Practice questions on Profit, Loss and Overhead Expenses

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 loss of 15% on an article with cost price Rs 600 gives a selling price of:
(a) Rs 90 (b) Rs 690 (c) Rs 510 (d) Rs 585
Hint
$S P = 600 \times \frac{85}{100}$ .
Answer
(c)
Q2 · 2 marks · Short answerBoard level
An article bought for Rs 750 is sold at a loss of 8%. Find the selling price.
Hint
Multiply by 92 over 100.
Answer
$S P = 750 \times \frac{92}{100} = 690$ . Rs 690.
Q3 · 3 marks · Short answerHarder board level
Kavita buys a second-hand scooter for Rs 18,000, spends Rs 2,000 on repairs and sells it at a profit of 10%. Find the selling price and the profit.
Hint
CP includes the repair cost.
Answer
CP $= 20000$ ; SP $= 20000 \times 1.10 = 22000$ ; profit $= 2000$ .
Q4 · 4 marks · Short answerHarder board level
By selling an article for Rs 1,980 a shopkeeper loses 12%. At what price should he sell it to gain 12%?
Hint
Find CP first.
Answer
CP $= 1980 \times \frac{100}{88} = 2250$ . For 12% gain: $2250 \times 1.12 = 2520$ . Rs 2520.
Q5 · 4 marks · Long answerHOTS / competency
A sells an article to B at a profit of 10%, and B sells it to C at a profit of 20%. C pays Rs 2,640. Find what A paid for it.
Hint
Work backwards one step at a time.
Answer
B's CP $= 2640 \times \frac{100}{120} = 2200$ . This is A's SP, so A's CP $= 2200 \times \frac{100}{110} = 2000$ . Rs 2000.

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 percent calculated?Show answer
The cost price.
2.What is the effective cost price?Show answer
Purchase price plus overhead expenses.
3.CP from SP with 12% profit?Show answer
SP x 100/112.
4.One article gains 20%, another loses 20% at same SP. Net?Show answer
A loss.

Profit, Loss and Overhead Expenses: ICSE Class 8 Maths Problems

Understand Profit, Loss and Overhead Expenses

Profit, Loss and Overhead Expenses: formulas to remember

How to solve Profit, Loss and Overhead Expenses questions

Profit, Loss and Overhead Expenses in real life

Tricks to remember Profit, Loss and Overhead Expenses

Profit, Loss and Overhead Expenses: solved examples

Where students lose marks in Profit, Loss and Overhead Expenses

Exam tips

Practice questions on Profit, Loss and Overhead Expenses

Test your recall

Profit, Loss and Overhead Expenses: frequently asked questions

Are overheads part of the selling price?

What if the question gives only a percentage and no price?