Before you delve into Profit and Loss concepts, take a few minutes to read this first and understand what every international student should know about building a good credit score.
Profit and Loss problems are directly relevant for not only entrance exams (like GMAT, GRE, CAT), but also for the MBA syllabus like Accounting, Financial Statements and more. In this article we cover the basic definitions, formulas, solved examples and wrap it up with some practice questions.
Profit and Loss | Definitions, Formulas, Solved Problems
Basic Definitions and Formulas
- Cost price (C.P.): This is the price at which an article is purchased.
- Selling price (S.P.): This is the price at which an article is sold.
- Profit or Gain: If the selling price is more than the cost price, the difference between them is the profit incurred.
Formula: Profit or Gain = S.P. – C.P.
- Loss: If the selling price is less than the cost price, the difference between them is the loss incurred.
Formula: Loss = Cost price (C.P.) – Selling Price (S.P.)
- Profit or Loss is always calculated on the cost price.
- Marked price: This is the price marked as the selling price on an article, also known as the listed price.
- Discount or Rebate: This is the reduction in price offered on the marked or listed price.
Below is the list of some basic formulas used in solving questions on profit and loss:
- Gain % = (Gain / CP) * 100
- Loss % = (Loss / CP) * 100
- SP = [(100 + Gain%) / 100] * CP
- SP = [(100 – Loss %) / 100]*CP
The above two formulas can be stated as,
If an article is sold at a gain of 10%, then SP = 110% of CP.
If an article is sold at a loss of 10%, then SP = 90% of CP.
- CP = [100 / (100 + Gain%)] * SP
- CP = [100 / (100 – Loss%)] * SP
Profit and Loss: Solved Examples
Question 1: An article is purchased for Rs. 450 and sold for Rs. 500. Find the gain percent.
Gain = SP – CP = 500 – 450 = 50.
Gain% = (50/450)*100 = 100/9 %
Question 2: A man sold a fan for Rs. 465. Find the cost price if he incurred a loss of 7%.
CP = [100 / (100 – Loss %)] * SP
Therefore, the cost price of the fan = (100/93)*465 = Rs. 500
Question 3: In a transaction, the profit percentage is 80% of the cost. If the cost further increases by 20% but the selling price remains the same, how much is the decrease in profit percentage?
Let us assume CP = Rs. 100.
Then Profit = Rs. 80 and selling price = Rs. 180.
The cost increases by 20% → New CP = Rs. 120, SP = Rs. 180.
Profit % = 60/120 * 100 = 50%.
Therefore, Profit decreases by 30%.
Question 4: A man bought some toys at the rate of 10 for Rs. 40 and sold them at 8 for Rs. 35. Find his gain or loss percent.
Cost price of 10 toys = Rs. 40 → CP of 1 toy = Rs. 4.
Selling price of 8 toys = Rs. 35 → SP of 1 toy = Rs. 35/8
Therefore, Gain = 35/8 – 4 = 3/8.
Gain percent = (3/8)/4 * 100 = 9.375%
Question 5: The cost price of 10 pens is the same as the selling price of n pens. If there is a loss of 40%, approximately what is the value of n?
Let the price of each pen be Re. 1.
Then the cost price of n pens is Rs. n and
the selling price of n pens is Rs. 10.
Loss = n-10.
Loss of 40% → (loss/CP)*100 = 40
Therefore, [(n-10)/n]*100 = 40 → n = 17 (approx)
Question 6: A dishonest merchant sells his grocery using weights 15% less than the true weights and makes a profit of 20%. Find his total gain percentage.
Let us consider 1 kg of grocery bag. Its actual weight is 85% of 1000 gm = 850 gm.
Let the cost price of each gram be Re. 1. Then the CP of each bag = Rs. 850.
SP of 1 kg of bag = 120% of the true CP
Therefore, SP = 120/100 * 1000 = Rs. 1200
Gain = 1200 – 850 = 350
Hence Gain % = 350/850 * 100 = 41.17%
Question 7: A man bought two bicycles for Rs. 2500 each. If he sells one at a profit of 5%, then how much should he sell the other so that he makes a profit of 20% on the whole?
Before we start, it’s important to note here that it is not 15% to be added to 5% to make it a total of 20%.
Let the other profit percent be x.
Then, our equation looks like this.
105/100 * 2500 + [(100+x)/100] * 2500 = 120/100 * 5000 → x= 35.
Hence, if he makes a profit of 35% on the second, it comes to a total of 20% profit on the whole.
Question 8: A shopkeeper allows a discount of 10% on the marked price and still gains 17% on the whole. Find at what percent above the cost price did he mark his goods.
Let the cost price be 100. Then SP = 117.
Let the marked price be x.
So, 90% of x = 117 → x = 130.
Therefore, he marked his goods 30% above the cost price.
Question 9: A shopkeeper offers a discount of 20% on the selling price. On a special sale day, he offers an extra 25% off coupon after the first discount. If the article was sold for Rs. 3600, find
- The marked price of the article and
- The cost price if the shopkeeper still makes a profit of 80% on the whole after all discounts are applied.
Let the marked price of the article be x.
First a 20% discount was offered, on which another 25% discount was offered.
So, 75% of 80% of x = 3600
75/100 * 80/100 * x = 3600 → x = 6000.
So the article was marked at Rs. 6000.
Cost price of the article = [100/(100+80)]*3600 = Rs. 2000.
It is important to note here that this DOES NOT equal to a 45% discount on the whole. When different discounts are applied successively, they CANNOT be added.
Profit and Loss Quiz: Practice Questions
Problem 1: Click here
If the loss incurred in a transaction is 3/5th of the selling price, find the loss percent.
Answer 1: Click here
Let the selling price be x. loss is 3x/5.
Cost price = Selling price + loss = x + 3x/5 = 8x/5
Loss% = (3x/5) / (8x/5) * 100 = 37.5%
Problem 2: Click here
After applying successive discounts of 10% and 5% on an article, it was sold at Rs. 513. Find the marked price of the article.
A. Rs. 590
B. Rs. 600
C. Rs. 603.5
Answer 2: Click here
90/100 * 95/100 * x = 513 → x = 600
Problem 3: Click here
A sells a set of books to B for Rs. 300 at a profit of 25%. B sells it to C at a loss of 10%.
i) What was the original price paid by A?
ii) What was the price paid by C to B?
A. 240, 260
B. 250, 270
C. 250, 260
D. 240, 270
Answer 3: Click here
i. Price paid by A (cost price paid by A) = [100/(100+25)]*300 = Rs. 240
ii. Price paid by C (Selling price by B to C) = [(100-10)/100]*300 = Rs. 270