Rahul earned 40 profit by selling his computer for a certain amount

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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.

Solution:

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%.

Solution:

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?

Solution:

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.

Solution:

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?

Solution:

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.

Solution:

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?

Solution:

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.

Solution:

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

1. The marked price of the article and
2. The cost price if the shopkeeper still makes a profit of 80% on the whole after all discounts are applied.

Solution:

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.

A. 37 B. 37.5 C. 37.75

D. None

Cost Price: The price at which an article is bought or purchased is called its cost price. (C.P.)

Selling Price: The price at which an article is sold is called its selling price. (S.P.)

Profit: When an article is sold for more than what it costs, we say that there is a ‘profit’ or gain.

Loss: When an article is sold for less than what it costs , we say that there is a ‘loss’.

When the selling price is equal to the cost price, then there is neither profit nor loss.

We recall a few important facts below:

1. Profit = Selling Price – Cost Price
2. Loss = Cost Price – Selling Price
3. Cost Price = Selling Price – Profit or, Selling Price + Loss
4. Selling Price = Cost Price + Profit or, Cost Price – Loss
5. Profit or Loss per cent =

Caution: Profit or loss per cent is never calculated on the number of items sold, but on the cost prices of the items.

In calculating any percentage change, the increase or decrease is expressed as a percentage of the first value. Buying comes before selling , thus, profit or loss is expressed as a percentage of the buying price ( i.e., the cost price ) and not of the selling price.

Overheads – If there are some additional expenses incurred on the transportation , repair etc of an article purchased, they are included in the C.P. of the article and are called ‘overheads’.

3 Major Type of Profit and Loss Problems

Type 1 : Find Profit or Loss Percent.

Example 1: What is the profit per cent if a table bought for is sold for ?

Solution:  A table is bought for and sold for .

Total profit

Profit % 

Example 2: Arun buys a T.V. for . The transportation charges are and the installation charges are . He then sells it to his friend for . Find the loss per cent.

Solution: .

Here transportation and installation charges fall under overhead costs.

More results on S.P. and C.P.:

1. If there is a profit of then,

2. If there is a loss of then,

From 1 and 2 , we derive that :

3. , when there is a profit of

4. , when there is a loss of

Type 2 : Find S.P. when C.P. and Profit (or loss) Percent Given

Example 1: A man bought a T.V. set for and he sold it at a profit of . Find the selling price.

Solution: Let the cost price be

Then, S.P. at a profit of

When C.P. is S.P. is

Then, When

Alternative Method:

where and

Example 2:  A man buys a cycle for and sells it at a loss of . Find the selling price of the cycle.

Solution: Let the C.P. be

Then, S.P. at a loss of

When

Then, when

Alternative Method:

 where loss and

Type 3 : Find Cost Price.

Example 1: Find the cost price of an article which is sold at a profit of for .

Solution: , Profit %

If , then

If , then

If , then

Alternative Method:

where

A few harder problems on profit and loss:

Example 1: By selling a plot of land for a person loses . At what price should he sell it so as to gain ?

Solution: On selling the plot for , he loses

He now wants a profit of of

Example 2: A man sells two watches at each. On one he gains and on the other he loses . What is his gain or loss per cent on the whole transaction ?

Solution: S.P. of the first watch , gain

C.P. of first watch

Similarly, C.P. of the second watch on which he loses

total C.P. of the two watches

And total S.P. of the two watches

net loss

Discount

Marked Price: The price printed on an article or on a tag tied to it or the advertised price or the listed price is called the marked price , or, M.P. of the article.

Sometimes to dispose of the old , damaged or perishable goods the retailers offer these goods at reduced prices. The retailers also reduce prices to increase the sale by reducing the marked prices of the articles. The amount deducted from the original marked prices is called ‘Retailer’s discount’ or simply ‘retail discount’ which is generally expressed as per cent or a fraction of the marked or original price.

Net Price (Selling Price): The price of an article after deducting discount from the marked price is called the net price of the article.

NOTE: Discount is always calculated on the marked price.

In solving the problems on discount, the following formula are generally used:

1.

2.

3. If discount is , then,

Example 1: The marked price of a pair of shoes is . The shopkeeper allows an off season discount of on it. Calculate – i) the discount and ii) the selling price.

Solution:  and

i)

ii)

Example 2: The marked price of an article is marked above the C.P. and then it is sold at a discount of . What is the net gain per cent ?

Solution: Let the of the article be

more than the

Exercise

1. A cloth merchant on selling of cloth obtains a profit equal to the selling price of of cloth. Find his profit per cent.
2. An article was sold at a loss of . Had it been sold for more, there would have been a profit of . Find the cost price.
3. A shopkeeper allows off on the marked price of an article and still gets a profit of . What is the marked price of the article when it’s cost price is ?
4. By selling bananas, a vendor loses the selling price of bananas. Find his loss per cent.
5. A tradesman allows a discount of on the marked price of goods. How much above the cost price must he mark his goods to make a profit of ?