Profit and Loss Notes for SSC Exams

Profit and Loss is one of the most repeated chapters in SSC Quantitative Aptitude. Two to four questions come from it in almost every Tier 1 paper, and the same ideas are used in discount, partnership and mixture questions. These profit and loss notes for SSC give you all the formulas, short tricks, solved examples and practice questions in one place.

Basic Terms

• Cost Price (CP): the price at which an article is bought.
• Selling Price (SP): the price at which an article is sold.
• Profit = SP - CP, when SP is more than CP.
• Loss = CP - SP, when CP is more than SP.
• Marked Price (MP): the price written on the article (list price).
• Discount = MP - SP, and it is always calculated on the marked price.
• Profit and loss percentages are always calculated on the cost price, unless the question says otherwise.

Important Profit and Loss Formulas

Marked Price and Discount

A shopkeeper first marks his goods above the cost price and then gives a discount. If the marked price is m% above CP and the discount is d%, then the net profit percentage is m - d - (m x d / 100). A profit of 26% in the example below comes from this formula: 40 - 10 - 4 = 26.

• Discount is always on the marked price, while profit is on the cost price.
• Selling at the marked price means the discount is zero.
• If a question says "successive discounts", use the formula d1 + d2 - d1d2/100.

False Weight and Dishonest Dealers

A dealer who says he sells at cost price but uses a lighter weight still makes a profit. The profit percentage equals Error / (True weight - Error) x 100. If a dealer sells 1000 g but gives only 900 g, the error is 100 g, so the profit is 100 / 900 x 100 = 11.11%.

Solved Examples

Example 1: A man buys an article for Rs 500 and sells it for Rs 600. Find the profit percentage.
Solution: Profit = 600 - 500 = 100. Profit % = 100 / 500 x 100 = 20%.

Example 2: An article is sold for Rs 1,080 at a profit of 8%. Find the cost price.
Solution: CP = SP x 100 / (100 + 8) = 1080 x 100 / 108 = Rs 1,000.

Example 3: The cost price of a bag is Rs 1,200. It is sold at a loss of 15%. Find the selling price.
Solution: SP = 1200 x (100 - 15) / 100 = 1200 x 85 / 100 = Rs 1,020.

Example 4: Two articles are sold at Rs 1,200 each. One is sold at 20% profit and the other at 20% loss. Find the overall result.
Solution: Both are sold at the same price with equal percentages, so there is a loss of 20 x 20 / 100 = 4%. Check: CP1 = 1000, CP2 = 1500, total CP = 2500 and total SP = 2400, so the loss is 100 / 2500 = 4%.

Example 5: A shopkeeper marks his goods 40% above the cost price and gives a discount of 10%. Find his profit percentage.
Solution: Profit % = 40 - 10 - (40 x 10 / 100) = 40 - 10 - 4 = 26%.

Example 6: The cost price of 20 articles is equal to the selling price of 16 articles. Find the profit percentage.
Solution: Profit % = (20 - 16) / 16 x 100 = 4 / 16 x 100 = 25%.

Quick Tips to Solve Faster

• Take CP = 100 for percentage questions, so that profit % directly gives the profit amount.
• If the same percentage is gained and lost on two equal-SP articles, the answer is always a loss of x squared / 100 %.
• Remember the multipliers: 20% profit = x 1.2, 25% profit = x 1.25, 10% loss = x 0.9, 20% loss = x 0.8.
• For "profit on SP", assume SP = 100 and find CP first, then convert to profit on CP.
• Use the single equivalent discount formula to compare two discount offers.

Common Mistakes to Avoid

• Calculating profit percentage on the selling price instead of the cost price.
• Calculating discount on the cost price instead of the marked price.
• Adding two successive discounts directly, without the d1d2/100 term.
• Forgetting that a profit and an equal loss on equal SPs always gives a net loss.
• Mixing CP and SP in the formula for a given profit or loss percentage.

Quick Revision Points

• Profit % = Profit / CP x 100.
• SP = CP x (100 + P) / 100 and CP = SP x 100 / (100 + P).
• Discount is on MP, and profit or loss is on CP.
• Successive discount = d1 + d2 - d1d2/100.
• Equal-SP articles with equal profit and loss percent: loss = x squared / 100 %.

Practice Questions With Answers

1. A man buys a pen for Rs 250 and sells it for Rs 300. Find the profit percentage.
   Answer: 20% (50 / 250 x 100).
2. An article is sold at a loss of 10% for Rs 540. Find the cost price.
   Answer: Rs 600 (540 x 100 / 90).
3. The cost price of an article is Rs 800. At what price must it be sold for a profit of 25%?
   Answer: Rs 1,000 (800 x 1.25).
4. Two successive discounts of 20% and 10% are equal to a single discount of?
   Answer: 28% (20 + 10 - 2).
5. An article is marked at Rs 500 and sold at a 12% discount. Find the selling price.
   Answer: Rs 440 (500 x 0.88).
6. A shopkeeper sells 1 kg of goods using a weight of 900 g. Find his gain percentage.
   Answer: 11.11% (100 / 900 x 100).
7. If the profit is 20% of the selling price, what is the profit percentage on the cost price?
   Answer: 25% (SP = 100, CP = 80, profit = 20).
8. The cost price of 18 articles equals the selling price of 15 articles. Find the profit percentage.
   Answer: 20% (3 / 15 x 100).
9. An article costing Rs 400 is marked up by 50% and sold at a 20% discount. Find the profit percentage.
   Answer: 20% (MP = 600, SP = 480).
10. An article is sold for Rs 700 at a loss of 12.5%. Find the cost price.
    Answer: Rs 800 (700 x 100 / 87.5).

How to Practise This Chapter

1. Learn the formulas in the table until you can write them without looking.
2. Solve the solved examples again on your own, without reading the solution.
3. Attempt the practice questions above with a timer of 10 minutes.
4. Solve the matching SSC profit and loss practice paper to test yourself in exam style.
5. Check the previous year papers to see how SSC frames this topic.

Related Notes and Practice Papers

• Percentage Notes
• Simple Interest Notes
• Ratio and Proportion Notes
• Average Notes
• SSC Profit and Loss Practice Paper

Explore More SSC Subjects

SSC exams test many subjects, so connect this topic with the related subjects below:

• Reasoning Notes
• Statistics Notes
• Indian Economy Notes
• English Notes
• General Awareness Notes
• All SSC subjects and notes

Frequently Asked Questions

What is profit and loss in simple words?

If you sell an article for more than you paid, you earn a profit. If you sell it for less than you paid, you suffer a loss.

How many questions come from profit and loss in SSC exams?

Usually two to four questions come from profit and loss in SSC CGL and CHSL Tier 1, and more if you count discount and false weight questions.

What is the formula for profit percentage?

Profit % = (Profit / Cost Price) x 100.

On which price is discount calculated?

Discount is always calculated on the marked price.

What is the formula for successive discount?

For two discounts d1 and d2, the single equivalent discount is d1 + d2 - (d1 x d2 / 100).

What happens when two articles are sold at the same price, one at a profit and one at a loss of equal percent?

There is always a loss of x squared / 100 percent, where x is the common percentage.

How is the profit of a dishonest dealer calculated?

Gain % = Error / (True weight - Error) x 100.

What is the difference between marked price and cost price?

Cost price is what the shopkeeper pays. Marked price is the price written on the article, which is usually higher than the cost price.

How can I solve profit and loss questions quickly?

Assume the cost price as 100 or a convenient number, use the multiplier method, and learn the standard shortcuts given in these notes.

Which chapters are related to profit and loss?

Percentage, ratio and proportion, simple interest, compound interest and partnership are closely related to profit and loss.