In this guide
Profit and loss questions are percentage questions with three prices in them: what the seller paid, what the seller asked, and what the buyer paid. Nearly every mistake comes from using the wrong one as the base. Once you know that profit is measured on cost and discount on the marked price, and you get used to setting the cost price at 100, most questions take three lines.
The three prices
| Term | Meaning | What is measured on it |
|---|---|---|
| Cost price (CP) | What the seller paid | Profit % and loss % |
| Marked price (MP) | The list or tag price | Discount % |
| Selling price (SP) | What the buyer actually paid | Nothing directly; it is the result |
- Profit = SP − CP, and profit % = profit ÷ CP × 100.
- Discount = MP − SP, and discount % = discount ÷ MP × 100.
Why profit is on CP: the question it answers is "how much did the seller gain on the money they put in?" Why discount is on MP: the discount is advertised off the tag price.
Methods that make it quick
Take CP = 100
With CP at 100, a 30% mark-up makes MP 130, a 10% discount makes SP 117, and the profit is simply 17%. No formula is needed, and the answer is already a percentage.
Link MP and CP directly
If a seller gives d% discount and still makes p% profit:
MP × (100 − d) = CP × (100 + p).
Both sides are the SP, written once from MP and once from CP.
Successive discounts
Two discounts of a% and b% equal a single discount of a + b − ab/100 per cent. This is the successive-change rule with both changes negative. Two discounts of 20% and 10% equal 28%, not 30%.
Same SP, same percentage gain and loss
If two items are sold at the same price, one at x% profit and one at x% loss, the overall result is always a loss of x²/100 per cent. The item sold at a loss had the higher CP, so the loss weighs more.
False weights
A seller who sells at cost price but gives less than the true weight gains
(true weight − given weight) ÷ given weight × 100.
The base is the weight given, because that is what the seller actually spent.
Worked examples
Example 1. CP is ₹640 and SP is ₹800. Find the profit per cent.
Profit = 160. 160 ÷ 640 = 1/4 = 25%.
Example 2. An item is marked 30% above cost and sold at a 10% discount. Find the profit per cent.
CP 100 → MP 130 → SP = 130 × 0.9 = 117. Profit 17%.
Example 3. Two items are each sold for ₹1,500, one at 25% profit and one at 25% loss. Find the overall result.
CPs: 1,500 ÷ 1.25 = 1,200 and 1,500 ÷ 0.75 = 2,000. Total CP 3,200; total SP 3,000.
Loss = 200 ÷ 3,200 = 6.25%. The shortcut gives 25²/100 = 6.25%.
Example 4. "Buy 5, get 1 free." Find the effective discount.
The buyer pays for 5 and takes 6. Discount = 1 ÷ 6 ≈ 16.67%. The base is the 6 items received, whose full price is the MP.
Example 5. Find the single discount equal to successive discounts of 20% and 10%.
20 + 10 − 200/100 = 28%. Check: 100 → 80 → 72.
Example 6. An item costs ₹800. At what price should it be marked so that the seller makes 20% profit after a 20% discount?
SP = 800 × 1.2 = 960. MP × 0.8 = 960, so MP = ₹1,200, which is 50% above cost.
Example 7. A shopkeeper sells at cost price but uses a 900 g weight for 1 kg. Find the gain per cent.
Gain = 100 ÷ 900 × 100 = 11.11%.
Example 8. The SP of 12 items equals the CP of 15 items. Find the profit per cent.
Let each item cost ₹1. Then 12 items sell for ₹15, so each sells for 15/12.
Profit on 12 items = 15 − 12 = 3, on a cost of 12. 25%.
A comparison of common set-ups
| Set-up | Quick result |
|---|---|
| Mark-up m%, discount d% | Profit = m − d − md/100 per cent |
| Successive discounts a%, b% | Single discount = a + b − ab/100 per cent |
| Same SP, x% profit and x% loss | Loss of x²/100 per cent |
| Buy n, get k free | Discount = k ÷ (n + k) × 100 |
| SP of a items = CP of b items | Profit = (b − a) ÷ a × 100 (a loss if b < a) |
Check the first row with Example 2: 30 − 10 − 300/100 = 17%.
Common mistakes
- Taking discount on CP or profit on MP.
- Adding successive discounts.
- Assuming equal profit and loss on equal SPs cancel out.
- In false-weight questions, dividing by the true weight instead of the weight given.
Practice set
- CP ₹450, SP ₹540. Profit per cent? 20%. 90 ÷ 450.
- MP ₹2,400, discount 12.5%. SP? ₹2,100. 12.5% = 1/8, and 2,400 ÷ 8 = 300.
- Marked 20% above cost, 5% discount. Profit per cent? 14%. 120 × 0.95 = 114.
- Single discount equal to 25% and 20% in succession? 40%. 25 + 20 − 5.
- Selling at ₹720 gives a 10% loss. At what price would the profit be 15%? ₹920. CP = 720 ÷ 0.9 = 800; 800 × 1.15 = 920.
- The loss on selling at ₹340 equals the profit on selling at ₹460. Find the CP. ₹400. CP is midway: (340 + 460) ÷ 2.
- The CP of 16 items equals the SP of 20 items. Profit or loss per cent? 20% loss. Each item sells for 16/20 = 0.8 of its cost.
- An item marked ₹1,500 is sold at 20% discount and still earns 20% profit. Find the CP. ₹1,000. SP = 1,200 = 1.2 × CP.
What to do next
- Solve ten profit and loss questions with CP = 100 before using any formula.
- Learn the comparison table above; each row is a one-line answer in the exam.
- Revise the base rules in percentage for LIC AAO.
- Move on to simple and compound interest, which uses the same successive-change idea.
A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Life Insurance Corporation of India website .
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