Profit & Loss is one of the most interesting topics in the Quants section. During the aptitude test, we can expect a good number of questions on this topic. To understand this concept clearly, we must know Percentages in detail.
The question type can be broadly classified as follows,
Let us understand Profit and Loss from the figures below.
Here are some of the most Important Formulas of Profit and Loss used in solving any question on profit and loss.
1) Gain = (S.P) – (C.P)
2) Loss = (C.P) – (S.P)
3) Loss or gain is always reckoned on C.P
Problem 1: The cost price of 18 lemons is equal to the selling price of 20 lemons. Find the gain or loss %.
18 lemons CP = 20 lemons SP
18 CP = 20 SP
SP = 18/20 CP
SP = 0.9 CP
Hence the loss of 10%
When there are two successive discounts on the same product, the initial value can be assumed as a hundred and the deduction can be made from it.
Problem 2: A man purchased a scooter for RS. 20000 and got it insured for 80% of its value. The scooter was totally destroyed in an accident and the insurance company paid him only 80% of the claimed amount. What was the loss suffered?
Let’s assume the amount of Rs. 20000 is 100%
1st deduction of 20% was made. Hence the remaining 80% was insured.
2nd deduction of 20% was made from the amount claimed. Hence 80% of 80 i.e. 64% of the amount was paid finally.
Loss suffered 100% – 64% = 36%
When two articles are bought for the same cost price, one at x% profit and the other at x% loss then the net profit or loss will be equal to 0%
Problem 3: A man buys two goats at Rs. 120 each. He sells one at a 25% gain and the other at a 25% loss. How much is his profit or loss?
Total cost price of two goats = 120 + 120 = Rs. 240
Total selling price of two goats = 120+Profit (25% of 120) +120- Loss (25% of 120)
= 150 + 90 = Rs. 240
When two articles are bought for the same selling price, one at x% profit and the other at x% loss then the net transaction ends in a loss of x2 / 100%
Problem 4: Rahul sells 2 flats for Rs. 198 each. On one transaction he loses 10% and on the other, he gains 10%. What is his profit or loss percentage?
Total selling price = 198 + 198 = Rs. 396
During 10% profit: SP = 1.1 CP 198 = 1.1 CP. Hence CP is Rs. 220
During 10% loss: SP = 0.9 CP 198 = 0.9 CP. Hence CP is Rs. 180
Total cost price = 220 + 180 = Rs. 400
Loss % = (4/400)*100 = 4% loss
It is important to remember that both the profit and loss are calculated from the Cost Price.
If a product was sold for 35% profit then the selling price of the product is 135% of CP. If the product is sold for 35% loss then the selling price is 65% of CP.
Problem 5: I buy two horses, A and B. A cost Rs. 50 more than B. I sell A at a profit of 16% and B at a profit of 7%. My total gain is Rs. 100. What was the original price of B?
Let’s say the price of B = X
Price of A = X + 50
Total gain is Rs. 100
Price of A – Price of B = 100
16% of (X+50) – 7% of X = 100
Hence X = Rs. 400.
False weight:
In order to gain profit sometimes, a false weight is used and the product is sold at the same price.
For example, 1000 grams costs Rs. 1000 but instead of the actual weight, only 800 grams are sold for Rs.1000.
Loss % = (Error/Actual price)*100.
These are the predominant varieties of problems asked in campus placements.
Q.6. Lalit marks up his goods by 40% and gives a discount of 10%. Apart from this, he uses a faulty balance, which reads 1000 gm for 800 gm. What is his net profit percentage?
Solution:
Let us assume his CP/1000 gm = Rs 100
So, his SP/kg (800 gm) = Rs 126
So, his CP/800 gm = Rs 80
So, profit = Rs 46
So, profit percentage = 46/80 x 100 = 57.5%
Q.7. A shopkeeper claims that he is selling sugar at Rs 23/kg which costs him Rs 25/kg but he is giving 800gm instead of 1000gm. What is his percentage profit or loss?
Solution:
Here the cost price of the sugar is Rs 25/kg and the selling price is Rs 23/kg. So the loss is Rs 2/kg and the loss percentage = 2/25 x 100 = 8%
The profit due to wrong weight = 200/800 x 100 = 25%
Hence the overall profit and loss are given by {P + Q + (PQ/100)}
But as he is making the loss of 8% in the first case we put -8 in the above expression. If the final value is positive then he is making a profit otherwise loss. So the net profit and loss =
{25 – 8 + {25 x (-8)}/100} = 25 – 8 – 2 = 15%
As the final value is positive he is making a profit of 15%.
Q.8. Let a dishonest shopkeeper sell sugar at Rs 18/kg which he has bought at Rs 15/kg and he is giving 800gm instead of 1000gm. Find his actual profit percentage.
Solution:
Here the cost price of the sugar = Rs 15/kg
The selling price = Rs 18/kg.
The profit made by the shopkeeper is Rs 3 and the profit percentage = 3/15 x 100 = 20%
This will be his total profit if he has sold 1 kg of sugar. But that is not the case here as he is using the false weight.
Now the profit due to wrong weight =
= (200/800)x100 = 25%
The overall profit percentage = {P + Q + (PQ/100)} = [20+25+{(20 x 25)/100}] = 50%
You can also attempt this problem by another method.
The cost price of 1kg of sugar is Rs 15. As the shopkeeper is giving only 800gm the cost price of the 800 gm sugar is Rs 12. Here we have calculated the cost price of 800gm sugar because the shopkeeper is selling only 800gm. He is selling 800 gm of sugar for Rs 18 for which he had paid Rs 12. So he gained Rs 6 and the profit percentage = 6/12 x 100 = 50%
The answer, in this case, is the same as calculated above but the first method is more easy than the second one. Just find the individual profits and put the values in {P + Q + (PQ/100)}
The above formula is also valid if the shopkeeper is making losses due to some reason. In that case, you will put the negative value for the loss. Let us take an example.
Example 2: A shopkeeper claims that he is selling sugar at Rs 23/kg which costs him Rs 25/kg but he is giving 800gm instead of 1000gm. What is his percentage profit or loss?
Solution: Here the cost price of the sugar is Rs 25/kg and the selling price is Rs 23/kg. So the loss is Rs 2/kg and the loss percentage = 2/25 x 100 = 8%
The profit due to wrong weight = 200/800 x 100 = 25%
Hence the overall profit and loss are given by {P + Q + (PQ/100)}
But as he is making a loss of 8% in the first case we put -8 in the above expression. If the final value is positive then he is making a profit otherwise loss. So the net profit and loss =
{25 – 8 + {25 x (-8)}/100} = 25 – 8 – 2 = 15%
As the final value is positive he is making a profit of 15%.