Chapter - 12
PROFIT AND LOSS
The concept of profit and loss is used to study the gain or loss in a business transaction. Whenever we purchase and sell an article we either earn profit or incur loss.
Cost price (CP): The price at which an article is purchased
Sale Price (SP): The price at which an article is sold.
Overhead charges: Apart from the actual cost price, if some charges have to be paid are called overhead charges. Such charges are freight, rent, salary of employees etc.
Profit (If SP > CP): If sale price of a commodity is more than the cost price, some profit is earned.
Loss (If SP < CP): When an article is sold at a price less than the cost price, loss is incurred.
1) Profit = Sale price – cost price
P = SP – CP
2) Loss = Cost price – Sale price
L = CP – SP
3) Profit % = (Profit / Cost Price) x 100
= (P / CP) x 100
4) Loss % = (Loss / cost price) x 100
= (L / CP) x 100
1) Profit or Loss is always on the cost price
2) If an article is sold at a certain gain (say 15%) then SP = 115 % of CP
3) If an article is sold at a certain loss (say 15%)
Then SP = 85% of CP
Example: 1) A person buys an article for Rs. 50 and sells it for Rs. 75. What will be his gain percent?
Solution: CP = Rs. 50 SP = Rs. 75
Gain = 75 – 50 =Rs. 25
We know that gain % = (gain /cp) x 100
= (25 / 50) x 100 = 50%
Example 2: A person buys an umbrella for Rs. 450 and sells it for Rs. 350/-. Find his loss %.
Solution: CP = Rs. 450 SP: Rs. 350
Loss = 450 – 350 =Rs. 100.
Loss percent = (Loss / CP) x 100
= (100 / 450) x 100 = 200/9 % =
Example 3: Find the sale price if CP is Rs. 160 and gain is 20%.
Solutions: SP = 120% of CP
= (120 / 100) x 160 = Rs. 192
Example 4: Find sale price when CP is Rs. 160 and loss is 20%.
Solution: SP = 80% of CP
Or SP = (160 x 80) / 100 = Rs. 128
Example 5: Find CP when SP Rs. 64 and loss is 20%
Solution: CP =
Example 6: Find CP when SP = 192 and profit is 20%
Solutions: CP =
Example 7: A chair is bought for Rs. 150 and sold at a gain of 8%. Find the selling price.
Solutions: SP =
Example 8: A bicycle is bought for Rs. 1500 and sold at a loss of 6%. Find the selling price.
Solutions: CP = 1500 Loss = 6%
Example 9: A table is sold for Rs. 1440 and there is a loss of 10%. At what price should it be sold to gain 10%.
Solutions: SP = Rs. 1440 Loss = 10%
So CP =
To find SP to gain 10%
CP = Rs. 1600 profit = 10%
Example 10: Ravi lost 20% by selling a watch at Rs. 1536. What will be his gain percent if he sells if for Rs. 2040.
Solution: SP = Rs. 1536 Loss = 20%
Now SP = Rs 2040, CP = 1920, gain = 2040 – 1920 = Rs 120
Gain percent =
Example 11: A shopkeeper sells an article at a profit of 20%. If he had bought it at 20% less and sold for Rs. 10 less, he would have gained 25%. Find the cost price of the article.
Solution: Let CP be 100 SP= 120
If the CP was 100 – 20 = Rs 80 and gain 25%
Old SP – New SP = Rs. 120 – 100 = Rs. 20
If there is a different of Rs. 20 CP = 100
Different of Rs. 10 CP = 50
Example 12: A person sells apples at 10 for a rupee and gains 20%. How many apples did he buy for a rupee.
Solution: In questions where some quantity of some article is bought or sold, profit or loss is on the quantity sold
Quantity sold is 10 apples
Profit = 20%
Profit on 10 apple is 20%
So profit =
It means he has saved 2 apples after selling 10. So he bought 12 for a rupee.
Example 13: A shopkeeper mixes 160 kg of rice at Rs. 27 per kg with 240 kg of rice at Rs. 32 per kg and sells the mixture to gain 20%. What is the sale rate of the mixture.
Solutions: Cost of 160 kg of rice @ Rs. 27 per kg.
= 160 x 27 = Rs. 4320
Cost of Rs. 240 kg of rice @ Rs. 32 per kg = 240 x 32 = 7680
Total = 7680 + 4320 = 12000
Now CP = Rs. 12000
Gain = 20%
So sale price kg = Rs. 36 per kg
Example 14: A man buys certain no. of oranges at the rate of 3 per rupee and the same number at 4 per rupee. He mixes then together and sells at 7 for two rupees. Find his gain or loss%.
Solution: LCM of 3 and 4 is = 12
Let us suppose he purchases
12 oranges at the rate of 3 a rupee. Money spent = Rs. 4
and 12 oranges at the rate of 4 a rupee = money spent = Rs. 3
so total oranges purchased = 24
and CP = Rs. 7
now he sells 24 oranges at the rate of 7 for Rs. 2
Loss = CP – SP = 7 -
% loss =
Technique to solve problems in a fast way
If a person sells two articles, one at a loss of x % and another at a gain of x%. then there is always a loss to the seller and the loss is equal to
Example 15: A man sells two horses for Rs. 4000 each. On one of the horses he loses 20% while on the other he gains 20%. Find his gain / loss percent in the whole transaction.
Solutions: Loss =
Example 16: The profit on selling an article for Rs. 1196 is equal to the loss on selling the same article for Rs. 1056. The cost price of the article is:
1) 1143 2) 1134
3) 1156 4) 1126
5) None of these
Solutions: Since gain and loss on selling the same article is equal, the cost price must lie at the middle of two sale prices.
On CP = = Rs. 1126
Example 17: On selling an article for Rs. 264 a man loses 4%. He should sell the article for how much so that his gain is 12%.
Solution: SP is given to be = Rs. 264
Loss = 4%
So CP =
Now the gain he wants is 12%
So the SP =
Example 18: If the selling price of 10 pens is the same as the cost price of 8 pens. Find the gain or loss percent.
Solution: In such like questions, when cost price and the selling price is the same and quantities sold and purchased is given, the profit / loss is on the quantity sold.
For some money he purchased 8 pens and sold 10 pens for the same amount. It means he lost 2 pens.
So on 10 pens he has lost 2 pens. on 100, he has lost
2/10 x 100 = 20 pens
So los is 20%
Example 19: On selling 100 mangoes, a person gains the SP of 20 mangoes. Find his gain percent.
Solution: Let the SP of 100 mangoes be Rs. 100
He saves the SP of 20 mangoes which is equal to Rs. 20
So gain = Rs. 20
CP = Rs. 100 – Rs. 20 = Rs. 80
Gain % = 20/80 x 100 = 25%
Example 20: On selling a shaving machine for Rs. 1530, the loss is 10%. What will be the gain percent if the machine is sold for Rs. 1819.
Solutions: 1st SP = Rs. 1530
Loss = 10%
Now 2nd SP = Rs. 1819
Gain = Rs. 1819 – Rs. 1700 = s. 119
Example 21: A trader allows a discount of 15% of the marked price on his article. How much above the cost price should he mark the price to gain 19%.
Solution: let the marked price be Rs. 100.
Discount = 15%
SP = 100 – 15= 85
He wants to make a profit of 19%
So his CP should be
If the CP is 8500/119 he should mark Rs. 100
If the CP is 1 he should mark Rs. 100 x (119 / 8500)
If the CP is 100 he should mark Rs. =
He should mark the price 40% more than the CP.
Example 22: I purchased an item for Rs. 8200 and sold it at a gain of 25%. From the sale price of the item I purchased another item and sold it at a loss of 20%. What will be the overall Gain or loss.
Solutions: CP = Rs. 8200
Gain = 25%
Again CP = 10250
Loss % = 20%
So there will not be any loss or gain.
Example 23: The cost price of an item is two third of its selling price. What is the gain / loss percent?
Solution: let CP = Rs. 100
Then SP =
Gain % = = 50%
Example 24: Apples are bought at 6 for Rs. 5 and sold at 8 for Rs. 11. Find the gain or loss per cent.
Solution: Let the no. of apples purchased and sold be 24 (LCM of 6 and 8)
CP of 24 apples = Rs. 20
SP of 24 apples = Rs. 33
Gain = Rs. 33 – Rs. 20 = Rs. 13
So gain % =
Example 25: Find a single discount equivalent to three successive discounts of 10%, 20% and 40%.
Solution: On Rs. 100, 10% discount is given so SP = 100 – 10 = 90
20% discount on Rs. 90 =
The balance amount is 90 – 18 = 72
40% of discount on Rs 72 =
Balance amount is 72 -
Total discount = 100 - = 56.8%