1. Basics
- Profit = SP − CP; Loss = CP − SP. Profit% and loss% are always on CP.
- SP = CP × (100 + P%)/100; CP = SP × 100/(100 + P%).
2. Standard types
| Type | Rule |
|---|---|
| Two articles sold at the same SP, one at x% gain, other at x% loss | Always a loss of x²/100 % |
| CP of x articles = SP of y articles | Profit% = (x − y)/y × 100 |
| Dishonest dealer uses false weight | Gain% = error/(true value − error) × 100 |
| Marked price and discount | SP = MP × (100 − d)/100 |
| Buy at x for ₹1, sell at y for ₹1 | Gain% = (x − y)/y × 100 |
| Chain (A sells to B at a%, B to C at b%) | C's price = A's CP × (1 + a/100)(1 + b/100) |
3. Solved examples
CP ₹400, gain 15% → SP = 400 × 1.15 = ₹460.
Two TVs sold at ₹9,900 each, one at 10% gain, other at 10% loss → loss 1% overall.
CP of 20 pens = SP of 16 pens → profit = 4/16 = 25%.
A dealer uses 900 g for 1 kg → gain = 100/900 = 11 1/9%.
(ASO 2021) 11 oranges for ₹10 and sells 10 for ₹11 → (11/10)/(10/11) = 121/100 → 21% gain.
By selling at ₹720 a man loses 10%; to gain 10% he must sell at 720 × 110/90 = ₹880.
A sells to B at 20% gain, B to C at 10% gain; C pays ₹264 → A's CP = 264/(1.2 × 1.1) = ₹200.
Solved examples by question type
Each type that comes in the ASO paper, worked step by step. Try it yourself first, then read the solution.
Basic level
Example 1. An article bought for ₹2,000 is sold for ₹1,700. The loss percent is:
(a) 17.65% (b) 20% (c) 15% (d) 30%
Answer: (c) 15%
Solution: Loss = 300. Loss % = 300/2,000 × 100 = 15%. Always on CP.
Example 2. A shopkeeper buys a fan for ₹600 and wants a loss of 5%. He should sell it for:
(a) ₹650 (b) ₹630 (c) ₹570 (d) ₹595
Answer: (c) ₹570
Solution: SP = 600 × 95/100 = ₹570.
Example 3. A shopkeeper buys a fan for ₹1,250 and wants a loss of 12%. He should sell it for:
(a) ₹1,100 (b) ₹1,125 (c) ₹1,370 (d) ₹1,400
Answer: (a) ₹1,100
Solution: SP = 1,250 × 88/100 = ₹1,100.
Example 4. By selling a watch for ₹1,200, a man loses 20%. The cost price of the watch is:
(a) ₹1,440 (b) ₹1,200 (c) ₹1,500 (d) ₹1,600
Answer: (c) ₹1,500
Solution: CP = SP × 100/(100 − 20) = 1,200 × 100/80 = ₹1,500. Do not take 20% of SP.
ASO exam level
Example 5. A man buys oranges at 3 for a rupee and sells them at 2 for a rupee. His gain percent is:
(a) 55% gain (b) 50% gain (c) 25% gain (d) 50% loss
Answer: (b) 50% gain
Solution: CP of 1 = 1/3, SP of 1 = 1/2. Ratio = 1.5 → 50%.
Example 6. A man bought toffees at 5 for a rupee. How many for a rupee must he sell to gain 25%?
(a) 4 (b) 7 (c) 5 (d) 8
Answer: (a) 4
Solution: CP of 1 = 1/5. SP of 1 = 1/5 × 125/100 = 1/4. So 4 for a rupee.
Example 7. A man sells two articles for ₹1,200 each. On one he gains 15% and on the other he loses 15%. Overall he:
(a) loses 15% (b) loses 2.25% (c) gains 2.25% (d) neither gains nor loses
Answer: (b) loses 2.25%
Solution: When two items are sold at the same price, one at x% gain and one at x% loss, there is always a loss of x²/100 = 2.25%.
Example 8. A shopkeeper claims to sell at cost price but uses a 800 g weight for 1 kg. His gain percent is:
(a) 20% (b) 27% (c) 25% (d) 11.11%
Answer: (c) 25%
Solution: He gives 800 g but charges for 1000 g. Gain = 200/800 × 100 = 25%.
Example 9. If an article is sold at 20% profit instead of 10% profit, the seller gets ₹75 more. The cost price is:
(a) ₹826 (b) ₹950 (c) ₹750 (d) ₹375
Answer: (c) ₹750
Solution: (20 − 10)% of CP = 75 → CP = 75 × 100/10 = ₹750.
Example 10. The ratio of the cost price to the selling price of an article is 3 : 4. The profit percent is:
(a) 10% (b) 38.33% (c) 25% (d) 33.33%
Answer: (d) 33.33%
Solution: Take CP = 3, SP = 4. Profit % = 1/3 × 100 = 33.33%.
Example 11. The cost price of 12 articles equals the selling price of 10 articles. The profit percent is:
(a) 2% (b) 25% (c) 16.67% (d) 20%
Answer: (d) 20%
Solution: Take CP of 1 = ₹1. SP of 10 = ₹12 → SP of 1 = 1.2. Profit = 20%.
Example 12. The cost price of 12 articles equals the selling price of 10 articles. The profit percent is:
(a) 16.67% (b) 25% (c) 2% (d) 20%
Answer: (d) 20%
Solution: Take CP of 1 = ₹1. SP of 10 = ₹12 → SP of 1 = 1.2. Profit = 20%.
Advanced level
Example 13. A man sells an article at 25% profit. Had he bought it at 25% less and sold it for ₹60 less, he would have gained 40%. The cost price is:
(a) ₹360 (b) ₹600 (c) ₹300 (d) ₹240
Answer: (c) ₹300
Solution: Let CP = 100. SP = 125. New CP = 75, new SP = 75 × 1.4 = 105. Difference 20 ↔ ₹60. CP = 100 × 60/20 = ₹300.
Example 14. A trader mixes goods costing in the ratio 3 : 2. He gains 12% on the first part and gains 8% on the second. His overall gain percent is:
(a) 10.4% (b) 7.4% (c) 10% (d) 12.4%
Answer: (a) 10.4%
Solution: Weighted average: (3×12 + 2×8)/5 = 10.4%.
Topic-wise practice for Profit and loss (Quant): CP of x = SP of y, profit on SP, articles bought and sold, dishonest shopkeeper. Useful for OPSC ASO, OSSC, OSSSC and other Odisha exams.
Question types covered
- CP, SP, profit and loss per cent
- Difference between SP and CP
- CP of x articles = SP of y articles
- Profit or loss on the selling price
- Bought at x per rupee, sold at y per rupee
- Two articles sold at the same price: one at profit, one at loss
- Selling in a chain (A to B to C)
- Dishonest shopkeeper and false weights
- Finding CP from the profit or loss given