 # Profit and Loss Percentage

Profit Percentage

Profit and Loss percentage is used to show the amount of profit and loss incurred in terms of percentage, which can be a percentage of profit or percentage of loss. Also, as we all know, that percentage is one of those methods which are used for comparison of two qualities. In our day to day life, we come across a lot of situations where we calculate or compare anything in "per-cent." Here are some common examples: let relate the percentage of your results; everyone compares your results with your classmates or your partners.

Profit and Loss Percentage Example

Another most common example is related to buying and selling of goods. To calculate profit or loss on an item, one has to calculate it in percentage.

So, here in this article, we are going to discuss the concepts and importance of percentage in profit and loss.

To learn the concept of profit and loss percentage, we need to memorize terminologies for sales and purchase of goods.

Cost Price (CP)

The price at which the item is purchased by us is known as the cost price. It is given by CP.

Selling Price (SP)

The price at which the item/good can be sold is known as selling price. It is denoted or given by SP.

Note: The profit or loss of a product during the sales and purchase of an item depends completely on cost price and selling price.

Profit Percentage

If the cost price of an item is less than the selling price, this is the only condition for profit on the item.

SP > CP

Net Profit

The net profit can be calculated as the difference between the selling price and cost price.

[ Net Profit = SP - CP]

Profit Percentage Formula

${\text{Profit % = }}\frac{{SP - C.P.}}{{C.P.}} \times 100 = \frac{{Net{\text{ Profit}}}}{{C.P.}} \times 100$

Loss Percentage

If the cost price of the item is more than the selling price of the item, then the item is said to be sold at a loss.

SP < CP

Net Loss

Net Loss can be calculated as the difference between the cost price and selling price.

[ Net Loss = CP - SP]

Loss Percentage Formula

Loss % = [(CP - SP)/CP] x 100 = [(Net loss)/CP] x 100

 Note- It is strictly noted that the Profit Loss percentage is calculated on the Cost Price of the item, until and unless it is mentioned to calculate percentage on Selling Price.

Questions:

Question 1.   Find whether the following transactions are in profit or loss. Also, find the profit  loss percent  for each case.

(i)   A General knowledge book was bought for Rs 250 and sold for Rs 325

(ii)  Ranveer bought a motorcycle for Rs 12,000 and sold  the same for Rs 13,500

(iii)   A cupboard bought for Rs 2,500 and sold at Rs 3,000

(iv)  A skirt bought for Rs 250 and sold at Rs 150

Solution:

(i)    C.P = RS 250

S.P = Rs 325

Here, S.P > C.P

So,

Profit = S.P - C.P

= 325 - 250

= Rs 75

Profit Percentage =$\frac{{{\text{Profit}}}}{{C.P.}} \times 100\%$

= $\frac{{75}}{{250}} \times 100\%$

= $\frac{{75}}{{25}} \times 10\%$

= $\frac{{15}}{5} \times 10\%$

= 3 $\times$ 10%

= 30%

(ii)     C.P = Rs 12,000

S.P = Rs 13,500

Here S.P > C.P

So,

Profit = S.P - C.P

= Rs 13,500 - 12,000

= Rs 1,500

Profit Percentage = $\frac{{{\text{Profit}}}}{{C.P.}} \times 100\%$

= $\frac{{1,500}}{{12,000}} \times 100\%$

= 15/120 $\times$ 10%

= 15/12 $\times$10%

= 5/4 $\times$ 10%

= 5/2 $\times$ 5%

= 25/2%

= 12.5%

(iii)     C.P = Rs 2,500

S.P = Rs 3,000

Here S.P > C.P

So,

Profit = S.P - C.P

= Rs 3,000 - 2,500

= Rs 500

Profit Percentage = $\frac{{{\text{Profit}}}}{{C.P.}} \times 100\%$

= $\frac{{500}}{{2,500}} \times$100%

= 5/25 $\times$ 10%

= 1/5 $\times$10%

= 20%

(iv)     C.P = Rs 250

S.P = Rs 150

Here C.P > S.P

So,

Profit = C.P - S.P

= Rs 250 - 150

= Rs 100

Loss Percentage =$\frac{{{\text{Loss}}}}{{C.P.}} \times 100\%$

=$\frac{{100}}{{250}} \times$ 100%

= 10/25 $\times$ 10%

= 2/5 $\times$10%

= 2 $\times$ 20%

= 40%

Question 2.    Juhi sells a washing machine for Rs 13,500. She loses 20% in the bargain. At what price Juhi bought the washing machine?

Solution:

S.P = Rs 13,500

C.P = ?

Loss Percentage = 20%

Now,

Loss = C.P - S.P

C.P =S.P + Loss

C.P = 13,500 + Loss           ….(i)

Loss Percentage =$\frac{{{\text{Loss}}}}{{C.P.}} \times$ 100%

Cross Multiplying

1 $\times$ (13,500 + Loss) = 5$\times$ Loss

13,500 + Loss = 5 Loss

5 Loss = 13500 + Loss

5 Loss - Loss = 13500

4 Loss = 13500

Loss  = $\frac{{13,500}}{4}$

Loss =  Rs 3,375

From (i)

C.P = 13500 + 3375

= Rs 16875

So, she bought it at Rs 16,875

Question 3.    2. Ron purchased a table for Rs 1260, and due to some scratches on the top of the table, Ron has to sell it for Rs 1197. Find the loss percent.

Solution:

CP =  Rs.1260

SP = Rs 1197.

Since,

(SP) < (CP), Ron makes a loss.

Loss = Rs (1260 - 1197)

= Rs 63.

Loss Percentage = $\frac{{{\text{Loss}}}}{{C.P.}} \times$ 100%

= [(63 / 1260) × 100] %

= 5%

While calculating profit percent and loss percent for an article, sometimes, after purchasing the article, one has to pay some more money for transportation, repairing charges, local taxes, etc. These extra expenses are known as overheads.

To calculate the total cost price, we have to add overheads to the purchase price.