Profit and Loss questions with answers and concepts

Learn profit and loss with concept notes and worked examples, then practise focused questions with explained answers. Build accuracy for placement and competitive aptitude tests before trying timed mode.

137 practice questionsPage updated 11 Nov 2026Review metadata pendingPractice questions

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Profit and Loss is a fundamental commercial mathematics topic that deals with calculating gains or losses incurred in business transactions. It involves understanding the relationship between Cost Price (CP), Selling Price (SP), Marked Price (MP), and various types of discounts. Mastery of this topic requires familiarity with percentage calculations and the ability to solve problems involving successive profits, losses, and combined transactions.

Key formulas and rules

11 rules

Profit: $Profit = S P - C P$ (when $S P > C P$ )

Loss: $Loss = C P - S P$ (when $C P > S P$ )

Profit Percentage: $Profit % = \frac{Profit}{C P} \times 100$

Loss Percentage: $Loss % = \frac{Loss}{C P} \times 100$

Selling Price with Profit: $S P = C P \times \frac{100 + Profit %}{100}$

Selling Price with Loss: $S P = C P \times \frac{100 - Loss %}{100}$

Cost Price from Profit: $C P = \frac{S P \times 100}{100 + Profit %}$

Cost Price from Loss: $C P = \frac{S P \times 100}{100 - Loss %}$

Discount: $Discount = M P - S P$

Discount Percentage: $Discount % = \frac{Discount}{M P} \times 100$

Selling Price with Discount: $S P = M P \times \frac{100 - Discount %}{100}$

Key concepts

Cost Price (CP) and Selling Price (SP)

Cost Price is the amount paid to purchase or manufacture an article. It includes all expenses incurred before the item is ready for sale. Selling Price is the amount at which an article is sold to the customer. The difference between SP and CP determines whether a transaction results in profit or loss. When SP > CP, there is a profit; when SP < CP, there is a loss.

Marked Price (MP) and Discount

Marked Price, also called List Price, is the price tagged on an article by the seller. It is usually higher than the expected selling price to allow room for discounts. Discount is the reduction given on the Marked Price to attract customers. The actual selling price is calculated after deducting the discount from the marked price: SP = MP - Discount.

Successive Profits and Losses

When multiple profits or losses occur in sequence, they compound. For successive profits of $a %$ and $b %$ , the overall profit is $(a + b + \frac{ab}{100}) %$ . For a profit of $a %$ followed by a loss of $b %$ (or vice versa), the unified formula is $(a - b - \frac{ab}{100}) %$ , where a positive result indicates net gain and a negative result indicates net loss. Successive discounts of $d_{1} %$ and $d_{2} %$ yield a single equivalent discount of $(d_{1} + d_{2} - \frac{d _{1} d _{2}}{100}) %$ .

False Weight Problems

In false weight problems, a merchant claims to sell goods at a certain weight but actually uses a defective scale. If a seller claims to sell at cost price but uses a weight that is x% less than the actual weight, their profit percentage is [x / (100 - x)] x 100%. This concept tests understanding of how measurement errors translate into hidden profits.

Overall Profit/Loss in Multiple Transactions

When dealing with multiple articles bought or sold together, calculate the total cost price and total selling price separately. The overall profit or loss is found by comparing these totals. For transactions where some items are sold at profit and others at loss, the net result depends on the quantities and individual percentages. Always verify whether the final outcome is profit or loss by comparing total CP and total SP.

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Worked examples

Example 1

A merchant bought 50 kg of rice at 40 per kg. He sold 30 kg at 45 per kg and the remaining 20 kg at 38 per kg. Find his overall profit or loss percentage.

Solution

Step 1: Compute total cost price (CP).

CP = 50 kg \times 40/ kg = 2, 000

Step 2: Compute total selling price (SP).

SP = (30 \times 45) + (20 \times 38) = 1, 350 + 760 = 2, 110

Step 3: Determine profit.

Profit = SP - CP = 2, 110 - 2, 000 = 110

Step 4: Compute profit percentage.

Profit % = \frac{Profit}{CP} \times 100% = \frac{110}{2 , 000} \times 100% = 5.5%

Answer: An overall profit of 5.5%.

Example 2

A shopkeeper marks his goods 25% above the cost price and allows a discount of 10% on the marked price. What is his actual profit percentage?

Solution

Step 1: Assume a cost price of 100.

CP = 100

MP = 100 \times (1 + 0.25) = 125

Step 2: Calculate selling price after 10% discount.

SP = 125 \times (1 - 0.10) = 125 \times 0.90 = 112.50

Step 3: Calculate profit percentage.

Profit % = \frac{112.50 - 100}{100} \times 100% = 12.5%

Alternative successive formula:

Profit % = 25 - 10 - \frac{25 \times 10}{100} = 15 - 2.5 = 12.5%

Answer: 12.5%.

Example 3

A trader sells two articles at the identical selling price of 1,200 each. On one he gains 20% and on the other he loses 20%. Find his overall profit or loss percentage.

Solution

Step 1: Apply the standard identical-SP equal-percentage rule.
When two items are sold at the same selling price with equal gain and loss percentage $p$ , there is always an overall loss:

Loss % = (\frac{p}{10})^{2} % = (\frac{20}{10})^{2} % = 4%

Verification via individual Cost Prices:
- First article: $CP_{1} = \frac{1 , 200}{1.20} = 1, 000$
- Second article: $CP_{2} = \frac{1 , 200}{0.80} = 1, 500$
- Total $CP = 1, 000 + 1, 500 = 2, 500$
- Total $SP = 1, 200 + 1, 200 = 2, 400$
- $Loss = 2, 500 - 2, 400 = 100$

Loss % = \frac{100}{2 , 500} \times 100% = 4%

Answer: An overall loss of 4%.

Example 4

A dishonest trader claims to sell goods at cost price but uses a false weight of 900 grams instead of 1 kilogram. What is his profit percentage?

Solution

Step 1: Apply the false-weight gain formula.

Profit % = (\frac{Error}{True Weight - Error}) \times 100%

Step 2: Substitute error = $1000 - 900 = 100 g$ .

Profit % = \frac{100}{900} \times 100% = \frac{100}{9} % \approx 11.11%

Answer: Approximately 11.11% (or $11 \frac{1}{9} %$ ).

Representative solved questions

See the kind of question in this topic before opening the full practice set.

Question 1

By selling 12 oranges for Rs. 10, a man loses 20%. How many oranges should he sell for Rs. 25 to gain 25%?

20 oranges
22 oranges
25 oranges
24 oranges

Answer: D. 24 oranges

Explanation

SP of 12 oranges = Rs. 10 with 20% loss
CP of 12 oranges = 10/0.8 = Rs. 12.5
CP per orange = 12.5/12 = Rs. 1.0417
For 25% gain, SP per orange = 1.0417 x 1.25 = Rs. 1.302
Oranges for Rs. $25 = 25/1$ .302 ~= 19.2, checking options:
Alternatively: For 25% gain on $C P = R s$ . 12.5, need $S P = 15$ .625 for 12 oranges
For $S P = 25$ , oranges = (25 x 12)/15.625 = 24 oranges

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Question 2

An article is marked 40% above cost price and sold after giving two successive discounts of 10% each. What is the profit percentage?

13.4%
14%
13.6%
15%

Answer: A. 13.4%

Explanation

Let $C P = R s$ . 100
$M P = 100$ + 40% = Rs. 140
After first 10% discount = 140 x 0.9 = Rs. 126
After second 10% discount = 126 x 0.9 = Rs. 113.4
Profit = 113.4 - $100 = R s$ . 13.4
Profit% = 13.4%

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Question 3

A trader mixes 30 kg of rice at Rs. 20/kg with 20 kg at Rs. 30/kg and sells the mixture at Rs. 28/kg. What is his profit percentage?

12%
15%
20%
16.67%

Answer: D. 16.67%

Explanation

Total $C P = (30 \times 20) + (20 \times 30) = 600 + 600 = R s$ . 1200
Total quantity = 50 kg
$S P = 50 \times 28 = R s .1400$
Profit = 1400 - 1200 = Rs. 200
Profit% = (200/1200) x $100 = 16$ .67%

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Common mistakes and useful habits

Always identify and note down CP, SP, MP, and any discounts given in the problem before starting calculations.
When no specific values are given, assume CP = 100 for easier percentage calculations.
For successive profit/loss problems, use the formula (a + b + ab/100) or its variations rather than calculating step by step.
In false weight problems, remember the shortcut: Profit% = [Error / (True - Error)] x 100, where Error = True Weight - False Weight.
When two items are sold at the same price with equal profit and loss percentages, there is always an overall loss of (p^2/100)%.
For complex transactions involving multiple articles, calculate total CP and total SP separately rather than working with individual profit/loss percentages.

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Key concepts

Cost Price (CP) and Selling Price (SP)

Marked Price (MP) and Discount

Successive Profits and Losses

False Weight Problems

Overall Profit/Loss in Multiple Transactions

Check the idea while it is fresh.Open a focused exercise without losing this article.Practise this concept

Worked examples

Example 1

A merchant bought 50 kg of rice at 40 per kg. He sold 30 kg at 45 per kg and the remaining 20 kg at 38 per kg. Find his overall profit or loss percentage.

Solution

Step 1: Compute total cost price (CP).

CP = 50 kg \times 40/ kg = 2, 000

Step 2: Compute total selling price (SP).

SP = (30 \times 45) + (20 \times 38) = 1, 350 + 760 = 2, 110

Step 3: Determine profit.

Profit = SP - CP = 2, 110 - 2, 000 = 110

Step 4: Compute profit percentage.

Profit % = \frac{Profit}{CP} \times 100% = \frac{110}{2 , 000} \times 100% = 5.5%

Answer: An overall profit of 5.5%.

Example 2

A shopkeeper marks his goods 25% above the cost price and allows a discount of 10% on the marked price. What is his actual profit percentage?

Solution

Step 1: Assume a cost price of 100.

CP = 100

MP = 100 \times (1 + 0.25) = 125

Step 2: Calculate selling price after 10% discount.

SP = 125 \times (1 - 0.10) = 125 \times 0.90 = 112.50

Step 3: Calculate profit percentage.

Profit % = \frac{112.50 - 100}{100} \times 100% = 12.5%

Alternative successive formula:

Profit % = 25 - 10 - \frac{25 \times 10}{100} = 15 - 2.5 = 12.5%

Answer: 12.5%.

Example 3

A trader sells two articles at the identical selling price of 1,200 each. On one he gains 20% and on the other he loses 20%. Find his overall profit or loss percentage.

Solution

Step 1: Apply the standard identical-SP equal-percentage rule.
When two items are sold at the same selling price with equal gain and loss percentage $p$ , there is always an overall loss:

Loss % = (\frac{p}{10})^{2} % = (\frac{20}{10})^{2} % = 4%

Loss % = \frac{100}{2 , 500} \times 100% = 4%

Answer: An overall loss of 4%.

Example 4

A dishonest trader claims to sell goods at cost price but uses a false weight of 900 grams instead of 1 kilogram. What is his profit percentage?

Solution

Step 1: Apply the false-weight gain formula.

Profit % = (\frac{Error}{True Weight - Error}) \times 100%

Step 2: Substitute error = $1000 - 900 = 100 g$ .

Profit % = \frac{100}{900} \times 100% = \frac{100}{9} % \approx 11.11%

Answer: Approximately 11.11% (or $11 \frac{1}{9} %$ ).

Representative solved questions

See the kind of question in this topic before opening the full practice set.

Question 1

By selling 12 oranges for Rs. 10, a man loses 20%. How many oranges should he sell for Rs. 25 to gain 25%?

20 oranges
22 oranges
25 oranges
24 oranges

Answer: D. 24 oranges

Explanation

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Question 2

An article is marked 40% above cost price and sold after giving two successive discounts of 10% each. What is the profit percentage?

13.4%
14%
13.6%
15%

Answer: A. 13.4%

Explanation

Let $C P = R s$ . 100
$M P = 100$ + 40% = Rs. 140
After first 10% discount = 140 x 0.9 = Rs. 126
After second 10% discount = 126 x 0.9 = Rs. 113.4
Profit = 113.4 - $100 = R s$ . 13.4
Profit% = 13.4%

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Question 3

A trader mixes 30 kg of rice at Rs. 20/kg with 20 kg at Rs. 30/kg and sells the mixture at Rs. 28/kg. What is his profit percentage?

12%
15%
20%
16.67%

Answer: D. 16.67%

Explanation

Total $C P = (30 \times 20) + (20 \times 30) = 600 + 600 = R s$ . 1200
Total quantity = 50 kg
$S P = 50 \times 28 = R s .1400$
Profit = 1400 - 1200 = Rs. 200
Profit% = (200/1200) x $100 = 16$ .67%

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Common mistakes and useful habits

Always identify and note down CP, SP, MP, and any discounts given in the problem before starting calculations.
When no specific values are given, assume CP = 100 for easier percentage calculations.
For successive profit/loss problems, use the formula (a + b + ab/100) or its variations rather than calculating step by step.
In false weight problems, remember the shortcut: Profit% = [Error / (True - Error)] x 100, where Error = True Weight - False Weight.
When two items are sold at the same price with equal profit and loss percentages, there is always an overall loss of (p^2/100)%.
For complex transactions involving multiple articles, calculate total CP and total SP separately rather than working with individual profit/loss percentages.

Key formulas and rules

Key concepts

Cost Price (CP) and Selling Price (SP)

Marked Price (MP) and Discount

Successive Profits and Losses

False Weight Problems

Overall Profit/Loss in Multiple Transactions

Worked examples

Example 1

Solution

Example 2

Solution

Example 3

Solution

Example 4

Solution

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Ready to test your understanding?

Keep building the same skill family.

Key formulas and rules

Key concepts

Cost Price (CP) and Selling Price (SP)

Marked Price (MP) and Discount

Successive Profits and Losses

False Weight Problems

Overall Profit/Loss in Multiple Transactions

Worked examples

Example 1

Solution

Example 2

Solution

Example 3

Solution

Example 4

Solution

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Ready to test your understanding?

Keep building the same skill family.