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Profit and loss for SSC CHSL

A fruit seller buys at one rate and sells at another, a trader sells to a trader, a dealer uses a false weight. Profit and loss questions in SSC CHSL follow a handful of patterns, and all of them are percentage questions on the cost price. The methods and why they work, seven worked questions and a practice set with solutions.

26 Sept 2026 6 min read

In this guide
  1. The basics, and why CP is the base
  2. Buying and selling in lots
  3. When CP of x items equals SP of y items
  4. Successive sales
  5. Two special cases worth knowing
  6. Seven worked questions
  7. Common mistakes
  8. Practice
  9. What to do next

Profit and loss questions describe everyday trading: a fruit seller, a shopkeeper, a trader who sells to another trader. Under the story, each one is a percentage question with one fixed rule. Profit and loss percentages are calculated on the cost price unless the question clearly says otherwise.

If you are comfortable with multipliers from the percentage guide, most of this topic is one or two multiplications. The rest is recognising a few standard setups, which this guide walks through.

The basics, and why CP is the base

  • Profit = SP − CP. Loss = CP − SP.
  • Profit % = profit ÷ CP × 100. Loss % = loss ÷ CP × 100.

Why CP: profit measures how much your money grew. You put in the cost price, so the growth is measured against it, just as a percentage increase is measured against the original value.

That means a profit of p% is simply an increase of p% on CP, and a loss of l% is a decrease of l%:

  • SP = CP × (100 + p)/100, and so CP = SP × 100/(100 + p).
  • SP = CP × (100 − l)/100, and so CP = SP × 100/(100 − l).

A useful check: selling at a profit of p% on CP is not the same as a profit of p% on SP. If a question ever says "profit on selling price", note it and use SP as the base for that question only.

Buying and selling in lots

When goods are bought "x for ₹a" and sold "y for ₹b", compare the price of one item, or use the LCM of x and y to avoid fractions.

Why the LCM works: choosing a quantity that divides evenly into both lots gives whole-number totals for both CP and SP. The profit percentage does not depend on how many items you imagine.

When CP of x items equals SP of y items

Profit % = (x − y)/y × 100. If y is larger than x, the same formula gives a negative value, which is a loss.

Why: take the CP of one item as ₹1. Then x items cost ₹x, and y items sell for ₹x, so one item sells for x/y. Profit on ₹1 is x/y − 1 = (x − y)/y.

Successive sales

When A sells to B and B sells to C, multiply the multipliers. A 20% profit followed by a 10% profit is × 1.2 × 1.1 = × 1.32, not × 1.30.

Two special cases worth knowing

Same selling price, equal profit and loss. If two items are sold at the same price, one at r% profit and the other at r% loss, the overall result is always a loss of r²/100 %.
Why: the item sold at a loss had the higher cost price, so the loss is on a bigger base than the gain. The two do not cancel.

False weights. A dealer who claims to sell at cost price but gives less weight earns error ÷ (true weight − error) × 100 %, where the error is how much weight is short.
Why: the customer pays for 1,000 g but the dealer's cost is only for what is actually handed over.

Seven worked questions

Q1. An article is sold for ₹1,150 at a profit of 15%. Find the CP.
CP = 1,150 × 100/115 = ₹1,000.

Q2. By selling a chair for ₹720, a trader loses 10%. At what price should it be sold to gain 10%?
CP = 720 × 100/90 = 800. Required SP = 800 × 1.1 = ₹880.
Shortcut: SP₂ = 720 × 110/90 = 880. You never need CP explicitly.

Q3. A person buys pens at 6 for ₹30 and sells them at 5 for ₹30. Find the gain percentage.
Take LCM(6, 5) = 30 pens. CP = 5 lots × ₹30 = ₹150. SP = 6 lots × ₹30 = ₹180. Profit = 30 on 150 = 20%.

Q4. The cost price of 20 articles equals the selling price of 16 articles. Find the profit percentage.
(20 − 16)/16 × 100 = 25%.

Q5. A sells a bicycle to B at 20% profit, and B sells it to C at 10% profit. C pays ₹5,280. What did A pay?
A's cost × 1.2 × 1.1 = 5,280, so A's cost = 5,280 ÷ 1.32 = ₹4,000.

Q6. A shopkeeper sells two phones at ₹1,200 each, one at 20% profit and the other at 20% loss. Find the overall result.
Formula: loss of 20²/100 = 4%.
Check: CP₁ = 1,200 ÷ 1.2 = 1,000 and CP₂ = 1,200 ÷ 0.8 = 1,500. Total CP 2,500, total SP 2,400, loss 100, which is 4% of 2,500.

Q7. A dealer claims to sell rice at cost price but uses a 900 g weight for 1 kg. Find the gain percentage.
The error is 100 g on 900 g actually given: 100/900 × 100 = 11 1/9%.

Common mistakes

MistakeFix
Calculating profit % on SPUse CP as the base unless told otherwise
Forgetting overheadsAdd repairs and transport to CP
Adding successive profits (20% + 10% = 30%)Multiply: 1.2 × 1.1 = 1.32
Assuming equal profit and loss cancelSame SP, r% up and r% down gives r²/100 % loss
Using the false weight as the baseDivide by the weight actually given

Practice

  1. A watch bought for ₹2,400 is sold for ₹2,760. Find the profit percentage.
  2. By selling an item for ₹450, a shopkeeper gains 12.5%. Find the CP.
  3. Bananas are bought at 12 for ₹30 and sold at 10 for ₹30. Find the gain percentage.
  4. The CP of 15 books equals the SP of 12 books. Find the gain percentage.
  5. A sells an item to B at a 10% loss, and B sells it to C at a 20% profit. C pays ₹1,080. What did A pay?
  6. Two items are sold for ₹990 each, one at 10% profit and the other at 10% loss. Find the overall profit or loss percentage.
  7. A dealer sells at cost price but uses an 800 g weight for 1 kg. Find the gain percentage.
  8. The profit on selling an article for ₹1,060 equals the loss on selling it for ₹940. Find the CP.

Answers:

  1. 15%. Profit 360 on 2,400.
  2. ₹400. 450 × 100/112.5.
  3. 20%. CP of one banana = ₹2.50 and SP = ₹3, so profit is 0.50 on 2.50.
  4. 25%. (15 − 12)/12 × 100.
  5. ₹1,000. The net multiplier is 0.9 × 1.2 = 1.08, and 1,080 ÷ 1.08 = 1,000.
  6. 1% loss. 10²/100 = 1. Check: CPs are 900 and 1,100, total 2,000, and SP total is 1,980.
  7. 25%. 200/800 × 100.
  8. ₹1,000. The CP is exactly halfway between the two prices: (1,060 + 940)/2.

What to do next

  • Write the four CP and SP formulas as multipliers and use only those for a week.
  • Solve 10 "lots" questions using the LCM method and 10 using the price of one item. Keep whichever is faster for you.
  • Learn the two special cases (same SP, false weight) with their reasons, not just the formulas.
  • Move on to discounts and marked price, which adds a third price to the same framework, and to mixtures, where profit on a mixture uses alligation.

A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Staff Selection Commission website .

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