Basic terms
CP = cost price, SP = selling price, MP = marked (list) price. Profit/loss percent is always on CP; discount percent is always on MP. Target: 40 seconds.
Key formulas
| Find | Formula |
|---|---|
| Profit % | (SP - CP)/CP x 100 |
| SP from profit % | CP x (100 + P)/100 |
| CP from SP | SP x 100/(100 + P) |
| SP after discount | MP x (100 - D)/100 |
| Relation | MP/CP = (100 + P)/(100 - D) |
| Successive discounts a%, b% | single discount = a + b - ab/100 |
| Same SP, gain x% and loss x% | always a loss of x²/100 % |
| False weight (gives g grams for 1 kg) | profit % = (1000 - g)/g x 100 |
Ready reckoner
- MP 25% above CP with 20% discount: 1.25 x 0.8 = 1, no profit no loss.
- MP 40% above CP with 10% and 15% successive discounts: 1.4 x 0.9 x 0.85 = 1.071, profit 7.1%.
- SP of x articles = CP of y articles: profit % = (y - x)/x x 100.
- Buy 4 get 1 free: discount = 1/5 = 20%.
Worked example
CP = Rs. 800. MP is 25% above CP and a 10% discount is given. Profit %?
MP = 1,000; SP = 900; profit = 100 on 800 = 12.5%.
Worked example 2 (dishonest dealer)
A shopkeeper uses a 900 g weight for 1 kg and sells at 8% above CP. Total profit?
Factor = 1.08 x 1000/900 = 1.2, so 20% profit. Or: 8 + 11.11 + 8 x 11.11/100 = 20.
Worked example 3 (two articles, same SP)
Two items sold at Rs. 9,900 each, one at 10% gain and one at 10% loss: overall loss = 1% of total CP. CPs are 9,000 and 11,000, so loss = Rs. 200.
Mains shortcut: convert every percentage to a multiplying factor (25% profit = x1.25, 12% discount = x0.88) and chain them. Most two-step problems become one line.
Common traps
- Taking profit % on SP instead of CP.
- Adding successive discounts (10% + 15% is not 25%).
- Assuming same CP when the question says same SP.
- Treating MP as CP.
Mains question types
- Profit on SP: if profit is 20% of SP, then with SP = 100, profit = 20 and CP = 80, so profit is 25% of CP.
- Gain expressed in articles: "selling 33 m of cloth gains the SP of 11 m" means 22 SP = 33 CP, so SP/CP = 3/2 and gain = 50%.
- Offers: "buy 2 get 1 free" is a 33.33% discount; "buy 3 get 2 free" is a 40% discount.
- Two items, one combined CP: write CP as x and (total - x), then form one equation with the overall profit.
- CP difference problems: express both CPs in terms of one variable (A = 1.2B), then use the SP difference.
Time target: 40 seconds in Prelims, 60 to 75 seconds for Mains multi-item questions.