About Profit and Loss
Every question in this topic rests on one rule with two halves: profit and loss percentages are calculated on the cost price, and discounts are calculated on the marked price. Fix those two bases and the rest of the topic is simple multiplication.
What you need to understand
- Profit is selling price minus cost price; loss is cost price minus selling price.
- Profit per cent and loss per cent are always calculated on the cost price.
- Discount is always calculated on the marked price, never on the cost price.
- There is neither profit nor loss when the selling price equals the cost price.
- A percentage profit can be converted into a multiplier: a profit of p% means the selling price is (100 + p)/100 times the cost price.
- Marking up and then discounting do not cancel out, because the two percentages are taken on different amounts.
Formulas to remember
How to work through these questions
- Write down which quantities the question gives you: cost price, selling price, marked price, profit per cent or discount per cent.
- Decide the base before calculating — cost price for anything to do with profit or loss, marked price for anything to do with discount.
- Turn the percentage into a multiplier: (100 + p)/100 for a profit, (100 - p)/100 for a loss or a discount.
- Move forwards by multiplying and backwards by dividing, instead of memorising a separate formula for every direction.
- Check the result makes sense: a profit must give a selling price above the cost price, and a discount must give a selling price below the marked price.
Mistakes that cost marks
- Calculating the profit percentage on the selling price instead of the cost price.
- Applying a discount to the cost price instead of the marked price.
- Adding a profit percentage to the cost price as though the percentage were a rupee amount.
- Assuming that marking up by 40% and then discounting by 40% leaves the price unchanged.
- Reporting the profit in rupees when the question asks for the profit per cent, or the reverse.
Worked example
An article bought for Rs. 800 is sold for Rs. 920. Find the profit per cent.
- Profit = SP - CP = 920 - 800 = 120.
- Profit per cent is calculated on the cost price, so the base is 800.
- Profit% = (120 / 800) x 100.
- 120 / 800 = 0.15, so the profit is 15%.
Answer: 15%
Practice questions with answers
A few Profit and Loss questions with the full solution shown, so you can see
how the method is applied before you attempt the timed set.
Question 1
Find the profit per cent when the cost price is Rs. 400 and the selling price is Rs. 556.
Answer: Option D — with explanation
Profit = SP - CP = 556 - 400 = 156.
Profit percent is always calculated on the cost price.
Profit% = \(\frac{156}{400}\) x 100 = 39%.
Common mistakes
- calculated the profit on the selling price instead of the cost price: 28.06
- computed the complement of the percentage: 61
- gave the profit in rupees instead of the percentage: 156
Question 2
The cost price of an item is Rs. 800. If it is sold at a gain of 16%, what is the selling price?
-
A
816
-
B
689.66
-
C
928
-
D
672
Answer: Option C — with explanation
Selling price = cost price + profit.
Profit = 16% of 800 = \(\frac{16}{100}\) x 800 = 128.
SP = 800 + 128 = 928.
Common mistakes
- divided by the profit factor instead of multiplying: 689.66
- added the percentage as rupees instead of taking the percentage of the cost price: 816
- subtracted the profit instead of adding it: 672
Question 3
Find the profit per cent when the cost price is Rs. 200 and the selling price is Rs. 236.
Answer: Option A — with explanation
Profit = SP - CP = 236 - 200 = 36.
Profit percent is always calculated on the cost price.
Profit% = \(\frac{36}{200}\) x 100 = 18%.
Common mistakes
- calculated the profit on the selling price instead of the cost price: 15.25
- computed the complement of the percentage: 82
- gave the profit in rupees instead of the percentage: 36
Question 4
Find the selling price when the cost price is Rs. 800 and the profit is 27%.
-
A
584
-
B
629.92
-
C
827
-
D
1016
Answer: Option D — with explanation
Selling price = cost price + profit.
Profit = 27% of 800 = \(\frac{27}{100}\) x 800 = 216.
SP = 800 + 216 = 1016.
Common mistakes
- added the percentage as rupees instead of taking the percentage of the cost price: 827
- divided by the profit factor instead of multiplying: 629.92
- subtracted the profit instead of adding it: 584
Question 5
The marked price of a shirt is Rs. 800. A discount of 5% is offered. Find the selling price.
Answer: Option D — with explanation
Discount is always calculated on the marked price.
Discount = 5% of 800 = 40.
Selling price = 800 - 40 = 760.
Common mistakes
- gave the discount amount instead of the selling price: 40
- treated the percentage as rupees: 795
- added the discount instead of subtracting it: 840
Frequently asked questions
Why is profit percentage calculated on the cost price?
Because that is the money the trader actually put in. The percentage answers the question of how much was earned on the investment, so the investment is the base.
Is discount calculated on the cost price or the marked price?
On the marked price. A discount is a reduction from the price displayed to the customer, so it is measured against that displayed price.
How do I find the selling price when I know the cost price and the profit per cent?
Multiply the cost price by (100 + profit%)/100. For a cost price of 800 and a profit of 15%, the selling price is 800 x 115/100 = 920.
What happens if a shopkeeper marks up 40% and then gives a 40% discount?
The shopkeeper makes a loss. Marking up 40% gives 140, and a 40% discount on 140 gives 84, which is below the original 100. The two percentages use different bases, so they do not cancel.
