COLOUR THEME
Cost price, selling price, marked price and discount, with the CP-to-SP table for quick work.
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This topic applies percentage to buying and selling. Profit and loss are always measured on the cost price (CP) unless the question says otherwise, and discount is always measured on the marked price (MP).
In brief
Covers Profit, Discount.
CP: cost price, the price at which an article is bought.
SP: selling price, the price at which it is sold.
MP: marked price or list price, the price printed on the article.
Profit when SP is more than CP. Loss when SP is less than CP.
Discount: the reduction offered on the marked price.
In brief
Concept Formula Profit SP - CP Loss CP - SP Profit percentage Profit/CP x 100 Loss percentage Loss/CP x 100 SP when there is a profit of P% CP x (100 + P)/100 SP when there…
| Concept | Formula |
|---|---|
| Profit | SP - CP |
| Loss | CP - SP |
| Profit percentage | Profit/CP x 100 |
| Loss percentage | Loss/CP x 100 |
| SP when there is a profit of P% | CP x (100 + P)/100 |
| SP when there is a loss of L% | CP x (100 - L)/100 |
| CP from SP at a profit of P% | SP x 100/(100 + P) |
| CP from SP at a loss of L% | SP x 100/(100 - L) |
| Discount | MP - SP |
| Discount percentage | Discount/MP x 100 |
| SP after discount d% | MP x (100 - d)/100 |
| MP when marked m% above CP | CP x (100 + m)/100 |
| Successive discounts d1% and d2% | Net discount = d1 + d2 - d1 d2/100 |
| Profit percentage after marking up m% and discounting d% | (100 + m)(100 - d)/100 - 100 |
| Overall result when two articles are sold at the same SP, one at x% gain and one at x% loss | Loss of x squared/100 % |
| Overall result when two articles have the same CP, one sold at x% gain and one at x% loss | No profit, no loss |
| If CP of x articles = SP of y articles | Profit % = (x - y)/y x 100 |
| Dishonest dealer using a false weight | Gain % = (true weight - false weight)/false weight x 100 |
In brief
Profit or loss CP : SP Profit 10% 10 : 11 Profit 20% 5 : 6 Profit 25% 4 : 5 Profit 12.5% 8 : 9 Profit 33.33% 3 : 4 Loss 10% 10 : 9 Loss 20% 5 : 4 Loss 25% 4 : 3 Loss 12.5% 8…
| Profit or loss | CP : SP |
|---|---|
| Profit 10% | 10 : 11 |
| Profit 20% | 5 : 6 |
| Profit 25% | 4 : 5 |
| Profit 12.5% | 8 : 9 |
| Profit 33.33% | 3 : 4 |
| Loss 10% | 10 : 9 |
| Loss 20% | 5 : 4 |
| Loss 25% | 4 : 3 |
| Loss 12.5% | 8 : 7 |
In brief
Example 1.
Example 1. An article bought for 450 is sold for 540. Find the profit percentage.
Example 2. An article sold at a loss of 15% fetches 680. Find the cost price.
Example 3. An article is marked at 1500 and sold after a 20% discount. If the CP is 1000, find the profit percentage.
Example 4. Two successive discounts of 20% and 10% are given on an article marked 1000. Find the final price and the single equivalent discount.
Example 5. Two articles are each sold for 2400, one at a 20% profit and the other at a 20% loss. Find the overall result.
CP of the first = 2400/1.2 = 2000. CP of the second = 2400/0.8 = 3000. Total CP = 5000, total SP = 4800.
Loss = 200, which is 4% of 5000. This matches the shortcut x squared/100 = 400/100 = 4%.
Example 6. The cost of 12 articles equals the selling price of 10 articles. Find the profit percentage.
Example 7. A sells an article to B at a 20% profit, and B sells it to C at a 25% profit. C pays 150. Find A's cost price.
Example 8. A shopkeeper marks goods 20% above the cost price and gives a 10% discount. Find the profit percentage.
Example 9. A dishonest dealer uses a 900 g weight for 1 kg. Find his gain percentage.
In brief
Covers Assume CP = 100, Successive transactions, Use the CP : SP ratio, Hidden MP.
Assume CP = 100 (or a convenient number such as 100 or 1000) to avoid fractions.
Successive transactions: multiply the multipliers (a 20% profit then a 25% profit = 1.2 x 1.25 = 1.5, so a 50% total profit).
Use the CP : SP ratio: if the ratio is 4 : 5, profit is 25%; if 5 : 4, loss is 20%.
Hidden MP: when the question gives only the discount and the profit, assume CP = 100 and work forward.
In brief
Covers false.
Computing profit percentage on SP instead of CP.
Computing discount on CP instead of MP.
Adding successive discounts.
Forgetting that a dishonest dealer's gain uses the false weight in the denominator.
Thinking that the same percentage gain and loss on the same SP gives no net result (it always gives a loss).
Practise with free MCQs and answer keys, then return here to fix what you got wrong.
↑ Module 4: Ratio, Percentage and Money · All 18 topics in Mathematical Reasoning · Unit overview and sample MCQs
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