Profit and Loss
Profit and Loss Problems for Placement and Aptitude Exams
Profit and loss is one of those topics that shows up everywhere — campus placements, bank exams, SSC, you name it. The concepts aren't complicated, but the questions are designed to trip you up with sneaky wording. Selling price of X items equals cost price of Y items? False weights? Successive discounts? These all follow a pattern once you know what to look for.
This article covers the key formulas and then walks through 24 practice problems with answers and solving hints.
The Core Formulas You Need
Basic relationships:
Profit = Selling Price (SP) − Cost Price (CP)
Loss = Cost Price (CP) − Selling Price (SP)
Profit % = (Profit ÷ CP) × 100
Loss % = (Loss ÷ CP) × 100
Finding SP or CP:
SP = CP × (1 + profit%/100)
SP = CP × (1 − loss%/100)
CP = SP ÷ (1 + profit%/100)
CP = SP ÷ (1 − loss%/100)
Successive discounts: If two discounts are x% and y%, the single equivalent discount = x + y − (xy/100)
False weight gain %: Gain% = (True weight − False weight) ÷ False weight × 100
Keep these handy while you practice. They cover 90% of what appears in exams.
Part 1: Problems Without Direct Answers (Solve These First)
Q1. The cost price of an article is ₹7,840. What should be the selling price to ensure a 7% profit?
Hint: SP = CP × (1 + profit%/100). Plug in CP = 7840 and profit = 7%.
✅ ₹8,388.80
Q2. A shopkeeper purchased 70 kg of potatoes for ₹420 and sold them at ₹6.50 per kg. What is the gain percentage?
Hint: Find total SP = 70 × 6.50. CP = 420. Gain% = (SP − CP) ÷ CP × 100.
✅ 8.33%
Q3. A gold ring was sold for ₹1,45,000 at a loss of 20%. What was its cost price?
Hint: SP = CP × (1 − loss%/100). Rearrange to find CP = SP ÷ (1 − 0.20).
✅ ₹1,81,250
Q4. By selling a paper for ₹28.50, a shopkeeper gains 14%. If the profit is reduced to 8%, what will be the new selling price?
Hint: First find CP using the 14% profit and ₹28.50 SP. Then calculate new SP using 8% profit on the same CP.
✅ ₹27.00
Q5. Find the single discount equivalent to successive discounts of 10%, 20%, and 30%.
Hint: Apply discounts one at a time on ₹100. After 10% → ₹90. After 20% → ₹72. After 30% → ₹50.40. Equivalent discount = 100 − 50.40.
✅ 49.6%
Q6. A dishonest dealer sells goods at cost price but uses 960 grams instead of 1 kg. What is his gain percentage?
Hint: Gain% = (True weight − False weight) ÷ False weight × 100 = (1000 − 960) ÷ 960 × 100.
✅ 4.17%
Q7. If the cost price of 15 books equals the selling price of 20 books, what is the loss percentage?
Hint: Let CP per book = x. Then 15x = 20 × SP → SP = 15x/20. Loss% = (CP − SP) ÷ CP × 100.
✅ 25%
Q8. A man buys pencils at 6 for ₹4 and sells them at 4 for ₹6. What is his gain percentage?
Hint: Find CP per pencil and SP per pencil. Gain% = (SP − CP) ÷ CP × 100.
✅ 125%
Q9. By selling 45 lemons for ₹40, a man loses 20%. How many should he sell for ₹24 to gain 20%?
Hint: Find CP of 1 lemon from the first scenario. Then find SP per lemon needed for 20% gain. Finally, how many lemons at that SP fetch ₹24?
✅ 18 lemons
Q10. A vendor loses the selling price of 4 oranges while selling 36 oranges. His loss is 10%. What was the cost price per orange?
Hint: Loss = SP of 4 oranges. Loss% = Loss ÷ CP × 100 = 10%. Use this to find CP of 36 oranges, then per orange.
✅ ₹1.25 per orange
Part 2: Problems with Answers
Q11. Mansi purchased a car for ₹2,50,000 and sold it for ₹3,48,000. What is the profit percentage?
Hint: Profit% = (SP − CP) ÷ CP × 100.
✅ 39.2%
Q12. CP = ₹2,569, SP = ₹2,272. What is the percentage of loss?
Hint: Loss% = (CP − SP) ÷ CP × 100.
✅ 11.56%
Q13. A gold bracelet is sold for ₹14,500 at a 20% loss. What was its original cost price?
Hint: CP = SP ÷ (1 − 0.20).
✅ ₹18,125
Q14. Shaloo sold a mobile for ₹1,950 at a 25% loss. At what price should she sell it for a 30% profit?
Hint: First find CP from the loss scenario. Then calculate new SP for 30% profit on that CP.
✅ ₹3,120
Q15. A book sold for ₹27.50 with a 10% profit. If sold for ₹25.75, what would the profit or loss percentage be?
Hint: Find CP from the first scenario. Then calculate profit/loss% for SP = ₹25.75.
✅ 6.36% profit
Q16. If the cost price is 96% of the selling price, what is the profit percentage?
Hint: CP = 0.96 × SP. Profit = SP − CP = 0.04 × SP. Profit% = Profit ÷ CP × 100.
✅ 4.17% profit
Q17. If the selling price of 30 items equals the purchase price of 25 items, what is the profit or loss percentage?
Hint: Let CP per item = x. Then SP per item = 25x/30. Compare SP to CP.
✅ 20% loss
Q18. A vendor buys bananas at 6 for ₹10 and sells at 4 for ₹6. What is the gain or loss percentage?
Hint: Find CP per banana and SP per banana. Compare them.
✅ 10% loss
Q19. A vendor buys buttons at 6 for ₹1. How many must he sell for ₹1 to gain 20%?
Hint: CP of 6 buttons = ₹1. Required SP for 20% gain = ₹1.20. At ₹1 selling price, how many buttons fetch ₹1.20 worth of value?
✅ 5 buttons
Q20. A dishonest dealer gains 6.25% by using a false weight. What weight does he use for 1 kg?
Hint: Gain% = (1000 − false weight) ÷ false weight × 100 = 6.25. Solve for false weight.
✅ 941 grams
Q21. An item listed at ₹150 is available for ₹105 after two successive discounts. If the second discount is 12.5%, what was the first discount?
Hint: Work backwards. Final price = ₹105, after 12.5% second discount → price before second discount = 105 ÷ (1 − 0.125). That's the price after first discount. Find first discount from list price ₹150.
✅ 16%
Q22. A man sold two flats for ₹6,75,958 each — gaining 16% on one and losing 16% on the other. What was the overall gain or loss?
Hint: When the same SP is used with equal gain% and loss%, there is always a net loss. Net loss% = (common %/10)² = 2.56%. Find total CP and then overall loss.
✅ Overall loss of ₹37,398 (approximately)
Q23. Two-thirds of a consignment was sold at 5% profit, the rest at 2% loss. Total profit = ₹400. What was the value of the consignment?
Hint: Let total value = x. Profit from first part = (2x/3) × 0.05. Loss from second part = (x/3) × 0.02. Net profit = 400. Solve for x.
✅ ₹15,000
Q24. An article is sold at a certain price. Selling it at 2/3 of that price causes a 10% loss. What is the gain % at the original price?
Hint: Let original SP = x. Then 2x/3 = CP × 0.90. Find CP in terms of x, then calculate gain% at SP = x.
✅ 35% gain
Common Mistakes to Avoid
The most common error is calculating profit or loss percentage on the selling price instead of the cost price. Always remember — profit% and loss% are always calculated on CP, not SP. The only exception is when a question specifically says "on SP," which is rare but does appear.
Successive discounts are another trap. You cannot simply add them. A 10% and 20% discount is not 30% — it's 28%. Always apply them one at a time, or use the formula.
For false weight problems, the denominator is the false weight, not the true weight. Getting that wrong flips the entire answer.
Wrap Up
Profit and loss questions are reliable marks in any aptitude test once you get the formula application right. The tricky ones — false weights, equal gain/loss on two items, SP equals CP of different quantities — all follow fixed patterns. Once you've solved a few of each type, you'll recognize them instantly in the exam.
For more reasoning practice, check out these also
For a structured placement prep roadmap explore,