# Calculating Profit Percent and Loss Percent | Profit and Loss Problems and Solutions

The profit and loss are the basic components of the income statement that summarizes the revenues, costs, and expenses subjected during a certain period. We use basic concepts in the calculation of profit percentage and loss percentage. Find Formulas for Calculating Profit % and Loss % and Problems on the Same in the forthcoming modules.

Cost Price (CP)

The price at which we purchase an item is called the cost price. In short, it is written as CP.

Example: A merchant bought an item at a cost of Rs. 150 and gain a profit of Rs. 30.

In the above example, Rs.150 is the cost price.

Selling Price (SP)

The price at which we sell an item is called the selling price. In short, it is written as SP.

Example: A shop keeper purchased a pen at Rs. 40 and he sold it at Rs.50 to a customer.

In the above example Rs. 50 is the selling price.

Profit or Gain

If the selling price of an item is more than the cost price of the same item, then it is said to be gain (or) profit i.e. S.P. > C.P.

Net profit= S.P. – C.P.

Loss

If the selling price of an item is less than the cost price of the same item, then it is said to be a loss i.e. S.P.  < C.P.

Net loss= C.P. – S.P.

NOTE:

It is important to note that the profit or loss is always calculated based on the cost price of an item.

## Profit and Loss Formulas for Calculating Profit % and Loss%

Have a glance at the Profit and Loss Formulas for finding the Profit and Loss Percentage. They are along the lines

• Net Gain = (S.P.) – (C.P.)
• Net Loss = (C.P.) – (S.P.)
• Gain % = (S.P. – C.P./C.P. *100)% = (gain/C.P. *100)%
• Loss % = (C.P. – S.P./C.P. *100)%  = (loss/C.P. * 100)%
• To find S.P. when C.P. and gain% or loss% are given :
• P. = [(100 + Gain %) /100] * C.P.
• P. = [(100 – Loss %) /100] * C.P.
• To find C.P. when S.P. and gain% or loss% are given :
• P. = [(100 + Gain %) /100] * S.P.
• P. = [(100 – Loss %) /100] * S.P.

### Profit and Loss Percent Questions and Answers

Question 1:

A man buys a book for Rs. 60 and sells it for Rs. 90. Find his gain/loss percentage?

Solution:

By seeing the question we can understand that the Selling price of the book is more than its cost price, therefore the man has profited on his total transaction.

Given data:

Cost price (C.P.) = Rs.60

Selling price (S.P.) =Rs. 90

Net profit = S.P. – C.P.

= 90 – 60

= 30

Profit % = ((Net profit)/C.P. *100)

= (30/60 *100)

= 50%

The total gain percentage is 50%.

Question 2:

If a fruit vendor purchases 9 oranges for Rs.8 and sells 8 oranges for Rs. 9. How much profit or loss percentage does he makes?

Solution:

By seeing the question we can understand that he bought 9 oranges at cost prices Rs.8 and sells 8 oranges at Rs. 9.

Given data:

Buying 9 oranges at Rs. 8

And Selling 8 oranges at Rs. 9

Here we are making quantities equal by multiplying the prices on both sides

We get,

Quantity            Price

Buying                 9 * 8                8 * 8

Selling                 8 * 9                9 * 9

By calculating,

Quantity            Price

Buying                 72                      64

Selling                 72                       81

By observing the above calculation we can see that the vendor bought 72 oranges for Rs. 64 while he sold 72 oranges at Rs. 81. This shows that the vendor is having profit in the entire transaction.

Profit percentage = ((S.P. – C.P.)/C.P. * 100)

= ((81-64)/64 * 100)

= 26.56 %

The total gain percentage for fruit vendors selling oranges is 26.56%.

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