Profit
When selling price is greater than cost price.
Profit = SP - CP
Profit% = Profit / CP x 100.
Quantitative Aptitude
Learn cost price, selling price, marked price, discount, dishonest weights, and successive transaction logic.
Profit and loss questions test whether you can move cleanly between cost price (CP), selling price (SP), marked price (MP) and discount. The essential idea is to express everything relative to one base — usually CP = 100 — and then reuse the same formula chain in every variant. Exam questions layer this with successive discounts, dishonest weights, and "sold two items at same price" tricks, so mastering the factor approach (SP = CP × progress factor) is the fastest route to accurate answers.
Profit and loss questions are base-sensitive. Profit percentage and loss percentage are always calculated on cost price unless the question says otherwise.
When selling price is greater than cost price.
Profit% = Profit / CP x 100.
When selling price is less than cost price.
Loss% = Loss / CP x 100.
Retail questions usually move from CP to marked price, then from marked price to SP after discount.
The listed price before discount.
If CP is 100 and markup is 40%, MP is 140.
Apply discount on marked price, not cost price.
MP 140 with 10% discount gives SP 126.
Memorize the high-frequency conversions and rate patterns so calculations become instant during timed tests.
| 10% profit | x 1.10 |
| 20% profit | x 1.20 |
| 25% profit | x 1.25 |
| 50% profit | x 1.50 |
| 10% loss | x 0.90 |
| 20% loss | x 0.80 |
| 25% loss | x 0.75 |
| 50% loss | x 0.50 |
Use when SP is greater than CP.
Use when SP is less than CP.
Useful when CP and profit percentage are known.
Use plus for profit and minus for loss.
The recurring question patterns in this topic — know the shape of each pattern before you solve.
Find profit or loss percent when CP and SP are given.
CP 500, SP 625 → profit 125 → 25%.
A single discount applied on MP; find effective profit.
Marked 35% above CP, discount 10% → profit 21.5%.
Two or more discounts applied in sequence; combine with factors.
10%, 20%, 30% → 0.9×0.8×0.7 = 0.504 → 49.6% discount.
Dealer sells less quantity at cost price and gains the hidden margin.
Using 900 g as 1 kg → gain 100/900 = 11.11%.
Two items sold at equal prices with equal gain and loss percentages.
Each at 20% → net loss of (20²/100) = 4%.
High-signal questions with full solution flow across difficulty patterns.
Classic exam problems worth internalizing — each one ships a complete step-by-step solution.
When two items are sold at the same SP, one at x% gain and one at x% loss, there is always loss.
Use when a seller uses a smaller weight but charges for the true weight.
Combine markup and discount as multiplying factors.
Where most students lose marks — review these before you sit the test.
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