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Study Materials › Arithmetic › Profit & Loss
Profit and loss questions are guaranteed marks — both the 2022 Constable and SI papers carried several. Almost every one reduces to keeping three quantities straight: cost price, marked price and selling price. Write down which one the question gives you before doing anything else.
Profit = SP − CP · Loss = CP − SP
Profit% = (SP − CP) / CP × 100 (always on cost price)
SP = CP × (100 + profit%) / 100
CP = SP × 100 / (100 + profit%)
Discount = MP − SP, and Discount% = (MP − SP) / MP × 100 (always on marked price)
| Situation | Result |
|---|---|
| Two successive discounts a% and b% | Net discount = a + b − ab/100 |
| Sold at same price, one at +x% and one at −x% | Always a net loss of x²/100 % |
| False weight (gives less than claimed) | Gain% = Error / (True value − Error) × 100 |
| Profit% on SP given, need profit% on CP | p/(100 − p) × 100 |
The marked price of an article is ₹800 and a customer buys it for ₹612 after two successive discounts. If the second discount is 15%, what was the first discount?
Work backwards from the final price. After the second discount of 15%, the customer pays 85% of the
intermediate price:
Intermediate price = 612 / 0.85 = 720.
First discount = (800 − 720) / 800 × 100 = 10%.
A shopkeeper sells an article by offering 24% discount on the marked price and thereby gets a loss of 5%. If he does not offer the discount, what is his gain or loss?
With the discount: SP = 0.76 × MP, and this equals 0.95 × CP.
So 0.76 MP = 0.95 CP, giving MP = 1.25 CP.
Without any discount he sells at MP = 1.25 CP, which is a 25% gain.
The cost price of an article is 64% of the marked price. If the article is sold at a 12% discount on the marked price, find the profit percent.
Take MP = 100. Then CP = 64 and SP = 88.
Profit = 88 − 64 = 24, so profit% = 24 / 64 × 100 = 37.5%.
Note: assuming MP = 100 rather than carrying symbols is almost always the fastest route.
A shopkeeper sells his goods at 30% profit on cost price. Due to an error, his weighing machine weighs 20% more than what it displays. Find his actual profit or loss.
The error works against the shopkeeper here — the customer receives more goods than paid for.
Suppose the display reads 1 kg; he actually hands over 1.2 kg. If cost is C per kg, his real cost is 1.2C
while he charges 1.3C.
Profit = 1.3C − 1.2C = 0.1C on a cost of 1.2C, so profit% = 0.1 / 1.2 × 100 =
8⅓% profit.
Also see: Percentages · Simple & Compound Interest · Time & Work