Profit, Loss and Discount
CSAT · Quantitative Aptitude
Introduction
Profit and loss questions are percentage questions with a business story. The single most important rule: profit and loss percentages are on cost price, discounts are on marked price.
Key concepts
Key terms
| Term | Meaning |
|---|---|
| CP | Cost price – what the seller paid |
| SP | Selling price – what the buyer pays |
| MP | Marked (list) price – printed price before discount |
| Profit % | (SP − CP)/CP × 100 |
| Discount % | (MP − SP)/MP × 100 |
Working with 100
Take CP = 100. A 25% markup gives MP = 125; a 20% discount on that gives SP = 100 → no profit, no loss.
Successive discounts
Discounts of a% and b% equal a single discount of a + b − ab/100 (20% and 10% = 28%, not 30%).
Same selling price, equal % profit and loss
If two articles sell at the same price, one at x% profit and the other at x% loss, the overall result is always a loss of x²/100 %.
Dishonest dealer
Selling at cost but giving less weight: profit % = (true weight − false weight)/false weight × 100. With a 900 g 'kilo', profit = 100/900 = 11.11%.
Buying n, getting m free
'Buy 4 get 1 free' is a discount of 1/5 = 20% on the price of five items.
- Profit % = (SP − CP)/CP × 100
- SP = CP × (100 ± p)/100
- Discount % = (MP − SP)/MP × 100
- Successive discounts: a + b − ab/100
- Equal SP, ±x%: loss x²/100 %
Solved examples
Example 1
Two successive discounts of 20% and 5% are equal to a single discount of:
(a) 24% (b) 25% (c) 26% (d) 21%
- Single discount = a + b − ab/100 = 20 + 5 − 100/100 = 24%.
Answer: (a) 24%
Example 2
Two successive discounts of 20% and 20% are equal to a single discount of:
(a) 40% (b) 38% (c) 36% (d) 33%
- Single discount = a + b − ab/100 = 20 + 20 − 400/100 = 36%.
Answer: (c) 36%
Example 3
A dishonest trader claims to sell at cost price but uses a 850 g weight instead of 1 kg. What is his profit per cent?
(a) 15% (b) 8.11% (c) 18.65% (d) 17.65%
- He gives 850 g but charges for 1000 g, gaining 150 g.
- Profit % = 150/850 × 100 = 17.65%.
Answer: (d) 17.65%
Example 4
Two successive discounts of 20% and 10% are equal to a single discount of:
(a) 28% (b) 30% (c) 25% (d) 31%
- Single discount = a + b − ab/100 = 20 + 10 − 200/100 = 28%.
Answer: (a) 28%
Example 5
Two articles are sold for ₹2400 each, one at 15% profit and the other at 15% loss. What is the overall result?
(a) profit of 2 1/4% (b) loss of 2 1/4% (c) loss of 15% (d) no profit, no loss
- When the selling prices are equal and the profit% equals the loss%, there is always a loss.
- Loss% = x²/100 = 15²/100 = 2 1/4%.
- Check: CPs are ₹2086.96 and ₹2823.53; total CP exceeds total SP.
Answer: (b) loss of 2 1/4%
Example 6
A dishonest trader claims to sell at cost price but uses a 800 g weight instead of 1 kg. What is his profit per cent?
(a) 20% (b) 25% (c) 11.11% (d) 26%
- He gives 800 g but charges for 1000 g, gaining 200 g.
- Profit % = 200/800 × 100 = 25%.
Answer: (b) 25%
Example 7
Two articles are sold for ₹1200 each, one at 30% profit and the other at 30% loss. What is the overall result?
(a) no profit, no loss (b) loss of 9% (c) loss of 30% (d) profit of 9%
- When the selling prices are equal and the profit% equals the loss%, there is always a loss.
- Loss% = x²/100 = 30²/100 = 9%.
- Check: CPs are ₹923.08 and ₹1714.29; total CP exceeds total SP.
Answer: (b) loss of 9%
Example 8
An article bought for ₹200 is sold for ₹160. What is the loss per cent?
(a) 20% (b) 22% (c) 25% (d) 10%
- Loss = 40.
- Loss% is always on cost price: 40 ÷ 200 × 100 = 20%.
Answer: (a) 20%
- Use CP = 100 for markup-and-discount questions.
- Multiply factors: markup 40% then discount 25% → 1.4 × 0.75 = 1.05 → 5% profit.
- For 'buy n get m free', discount = m/(n + m).
- Calculating profit % on SP.
- Adding successive discounts.
- Assuming equal profit and loss percentages cancel out.
Practice set
Attempt all 12 questions (about 90 seconds each), then check the worked solutions below.
Q1. An article bought for ₹500 is sold for ₹400. What is the loss per cent?
(a) 25% (b) 20% (c) 22% (d) 10%
Q2. A shopkeeper marks goods 40% above cost and gives a discount of 25%. What is his profit or loss per cent?
(a) profit 7.5% (b) profit 5% (c) loss 5% (d) profit 15%
Q3. A dishonest trader claims to sell at cost price but uses a 940 g weight instead of 1 kg. What is his profit per cent?
(a) 6% (b) 3.09% (c) 6.38% (d) 7.38%
Q4. An article bought for ₹800 is sold for ₹864. What is the profit per cent?
(a) 4% (b) 7 11/27% (c) 13% (d) 8%
Q5. A dishonest trader claims to sell at cost price but uses a 875 g weight instead of 1 kg. What is his profit per cent?
(a) 14.29% (b) 6.67% (c) 12 1/2% (d) 15.29%
Q6. An article bought for ₹640 is sold for ₹720. What is the profit per cent?
(a) 12.5% (b) 17.5% (c) 6.25% (d) 11 1/9%
Q7. An article bought for ₹500 is sold for ₹600. What is the profit per cent?
(a) 25% (b) 16 2/3% (c) 10% (d) 20%
Q8. A shopkeeper marks goods 50% above cost and gives a discount of 10%. What is his profit or loss per cent?
(a) profit 40% (b) profit 37.5% (c) profit 35% (d) loss 35%
Q9. Two articles are sold for ₹2400 each, one at 25% profit and the other at 25% loss. What is the overall result?
(a) loss of 25% (b) loss of 6 1/4% (c) profit of 6 1/4% (d) no profit, no loss
Q10. A shopkeeper marks goods 25% above cost and gives a discount of 10%. What is his profit or loss per cent?
(a) loss 12 1/2% (b) profit 13 1/2% (c) profit 15% (d) profit 12 1/2%
Q11. An article bought for ₹400 is sold for ₹500. What is the profit per cent?
(a) 25% (b) 20% (c) 30% (d) 12.5%
Q12. An article bought for ₹800 is sold for ₹720. What is the loss per cent?
(a) 15% (b) 5% (c) 10% (d) 11 1/9%
Q1 – (b) 20%. Loss = 100. Loss% is always on cost price: 100 ÷ 500 × 100 = 20%.
Q2 – (b) profit 5%. Take CP = 100. Marked price = 140. Selling price = 140 × 75/100 = 105. Result: 5% on cost.
Q3 – (c) 6.38%. He gives 940 g but charges for 1000 g, gaining 60 g. Profit % = 60/940 × 100 = 6.38%.
Q4 – (d) 8%. Profit = 64. Profit% is always on cost price: 64 ÷ 800 × 100 = 8%.
Q5 – (a) 14.29%. He gives 875 g but charges for 1000 g, gaining 125 g. Profit % = 125/875 × 100 = 14.29%.
Q6 – (a) 12.5%. Profit = 80. Profit% is always on cost price: 80 ÷ 640 × 100 = 12.5%.
Q7 – (d) 20%. Profit = 100. Profit% is always on cost price: 100 ÷ 500 × 100 = 20%.
Q8 – (c) profit 35%. Take CP = 100. Marked price = 150. Selling price = 150 × 90/100 = 135. Result: 35% on cost.
Q9 – (b) loss of 6 1/4%. When the selling prices are equal and the profit% equals the loss%, there is always a loss. Loss% = x²/100 = 25²/100 = 6 1/4%. Check: CPs are ₹1920 and ₹3200; total CP exceeds total SP.
Q10 – (d) profit 12 1/2%. Take CP = 100. Marked price = 125. Selling price = 125 × 90/100 = 112 1/2. Result: 12 1/2% on cost.
Q11 – (a) 25%. Profit = 100. Profit% is always on cost price: 100 ÷ 400 × 100 = 25%.
Q12 – (c) 10%. Loss = 80. Loss% is always on cost price: 80 ÷ 800 × 100 = 10%.
- Profit/loss on CP; discount on MP
- Take CP = 100
- Two discounts: a + b − ab/100
- Equal SP ±x% → loss x²/100
