Profit and Loss Mathematics : First of all, We will know about Profit and Loss Related basics, Cost Price, Selling Price, profit, Loss or Gain, Gain percentage and Loss percentage etc.

## Profit and Loss Mathematics : Clear your basic concepts

1. Purchasing Price : The amount for which an article is purchased is called its Purchase Price.

2. Overhead Expenses : Expenses incurred on the maintenance of the item and the cost to bring the item to the sales center or point.

3. Cost Price ( CP ) : [Purchasing Price + Overhead Expenses]

4. Selling Price (SP) : The amount for which an article is sold is called its Selling Price.

5. Profit or Gain : If (SP) > (CP) then there is a gain.
Hence, Profit or Gain = (SP) - (CP)

6. LOSS = If (CP) > (SP) then there is a loss.
Hence, Loss = (CP) - (SP)

Note : THE GAIN OR LOSS IS ALWAYS RECKONED ON THE COST PRICE.

7. DISCOUNT IS ALWAYS RECKONED ON THE FACE VALUE.

Now , We will learn about some basic and important Formulae related to Profit and Loss.

1. Selling Price = (CP) + (PROFIT)

2. Cost Price = (SP) - (Profit)

3. Profit or Gain = (SP) - (CP)

4. Loss = (CP) - (SP)

5. Cost Price = (SP) + (Loss)

6. Selling Price = (CP) - (Loss)

7. Gain percentage (Gain%) = [(gain*100)/CP]%

8. Loss Percentage (Loss%) = [(loss*100)/CP]%

9. Finding the SP when COST PRICE and Gain% or Loss% are given,

A. SP = [(100+gain%)/100]*CP

B. SP = [(100-loss%)/100]*CP

10. Finding the CP when SP and Gain% or Loss% are given,

A. CP = [100/(100+gain%)]*SP

B. CP = [100/(100-loss%)]*SP

#### NOW, Some Solved Examples based on these Formulae

Example 1.
Ramesh bought a TV for Rs. 1000 and sold it for Rs. 1500. Find his gain and gain per cent.

Solution : Given that, CP = 1000 and SP = 1500
Since  SP > CP
So, Ramesh makes a gain.
Gain = (1500 - 1000) = 500 Rs.
Gain% = [(500*100)/1000]% = 50%

Example 2.
Mohan bought an iron safe for Rs. 5580 and paid Rs. 170 for its transportation. Then, he sold it for Rs. 6440. Find the gain per cent earned by Mohan.

Solution : Given, Purchasing Price = 5580 Rs. And Overhead Expenses = 170 Rs.
So, Cost Price = (5580+170) Rs. = 5750 Rs.
Selling Price is given 6440 Rs.
Since, (SP) > (CP), Mohan makes a gain.
Gain = (6440 - 5750) = 690 Rs.
Gain% = [(690 * 100)/5750]% = 12%

Example 3. Given that Gain% 25 and CP 2000 Rs. Find the Selling Price.

Solution :
(Note : Remember the formula when CP and Gain% are given, how to find SP)
SP = [(100+25)/100] * 2000
Hence, Selling Price = 2500 Rs.

Example 4.
Shyam bought 20 kg of rice at Rs. 18 per kg and 25 kg of rice at Rs. 16 per kg. He mixed the two varieties and sold the mixture at Rs. 19 per kg. Find his gain per cent or loss per cent in the whole transaction.

Solution : @Rs. 18 per kg, The CP of 20 kg of rice is equal to (18 * 20) = 360 Rs.
And @Rs 16 per kg, The CP of 25 kg of rice is equal to (16 * 25) = 400 Rs.
Hence, Total of the CP = (360+400) = 760 Rs.
Now given that he sold the mixture @Rs. 19 per kg.
Total mixture = (20kg + 25kg) = 45 kg.
So, The SP = (45 * 19) = 855 Rs.
Here, (SP) > (CP), Shyam makes a gain.
Gain = (855 - 760) = 95 Rs.
Gain% = [(95 * 100)/760]% = (25/2)%

Example 5.
If the cost price of ten pens is equal to the Selling price of eight pens. Find the gain or loss per cent.

Solution : Let the cost price of each pen be Rs. x.
Then, CP of 8 pens = Rs. 8x
Given that, SP of 8 pens = CP of 10  pens = Rs. 10x
Thus, CP = Rs. 8x and SP = Rs. 10x.
Clearly there is a gain.
Gain = (10x - 8x) = 2x
Gain% = [(2x/8x)*100]% = 25%

Hope, that Profit and Loss Mathematics these Formulae and Examples based on it, will help you to solve the Profit and Loss Mathematics problems.