Your friend gives you Rs. 100 for a pen that you got for Rs. 90. You sell it to him and then buy a cricket bat from him for Rs. 3000. Later you find out that the bat was worth Rs. 2995. Did you lose money or did you make a profit? When you do a business transaction like selling things if you earn some amount in the transaction that amount is called the profit and if you lose some amount then it is called loss. Let’s compare some quantities with profit and loss.

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## Comparison Using Profit and Loss

**Cost Price:**The amount paid to purchase an article or the price at which an article is made is known as its cost price. The cost price is abbreviated as C.P.**Selling Price:**The price at which an article is sold is known as its selling price. The selling price is abbreviated as S.P.

## Profit

If the selling price (S.P.) of an article is greater than the cost price (C.P.), the difference between the selling price and cost price is called profit. Thus, if S.P. > C.P., then $$Profit = S.P. – C.P.\\ S.P. = C.P. + Profit \\ C.P. = S.P. – Profit $$

### Profit Percentage

The profit percent is the profit that would be obtained for a C.P. of Rs 100 i.e, $$Profit\quad percent=\left( \frac { Profit }{ C.P. } \right) \times 100$$

## Loss

If the selling price (S.P.) of an article is less than the cost price (C.P), the difference between the cost price (C.P.) and the selling price (S.P.) is called loss. Thus, if S.P. < C.P., then $$Loss = C.P. – S.P.\\ C.P. = S.P. + Loss\\ S.P. = C.P. – Loss$$

### Loss percentage

The loss percentage is the loss that would be made for a C.P. of Rs 100, that is $$Loss\quad percent=\left( \frac { Loss }{ C.P. } \right) \times 100$$

### Neutral Situation

If S.P. = C.P., then seller neither gain money or lose any.

## Solved Examples for You on Profit and Loss

### Example 1

A shopkeeper buys a toy for Rs 250 and sells it for Rs 285. Find his gain and gain percent.

**Solution: **We have, C.P. of the toy =Rs250 and S.P. of the toy = Rs285

Since S.P. > C.P .So, there is profit/gain given by:

$$Profit = S.P. – C.P.\\ Profit = Rs.285 – Rs.250\\ Profit = Rs.35$$

Now lets calculate gain in percentange:

$$Profit\; \%=\left( \frac { Profit }{ C.P. } \right) \times 100\\ Profit\; \%=\left( \frac { 35 }{ 250. } \right) \times 100\%\\ Profit\; \ %\quad =14 \%$$

Hence, Gain = Rs 35 and Gain% =14%

### Example 2

Rishi bought a wrist watch for Rs 2200 and sold it for Rs 1980. Find has loss and loss percent.

**Solution:** We have, C.P. of watch =Rs2200 and S.P. of watch =1980

Since S.P. < C.P. So, there is a loss given by

$$Loss=C.P.–S.P\\ Loss=Rs.2200-Rs.1980\\ Loss=Rs.220$$

Now, let’s calculate loss in percentage

$$Loss\quad percent=\left( \frac { Loss }{ C.P. } \right) \times 100\; %\\ Loss\; %=\left( \frac { 220 }{ 2200 } \right) \times 100\; %\\ Loss\; %=10%$$

Hence, Loss =Rs220 and Loss% =10%

### Example 3

Girl buys lemons at 4 for Rs 3 and sells them at 5 for Rs 4. How much percent loss or gain does she make if she sold total 20 lemon?

**Solution** – It is given that the girl buys lemons at 4 for Rs 3 and sells them at 5 for Rs 4. Therefore, to avoid frictions assume that the girl buys and sales 4 times 5= 20 lemons.

We have, $$C.P.\; of\; 4\; lemons=Rs3/-\\ C.P.\; of\; 1\; lemon=\; Rs\frac { 3 }{ 4 } /-\\ C.P.\; of\; 20\; lemons=Rs\frac { 3 }{ 4 } \times 20=Rs15/-\\ S.P.\; of\; 5\; lemons=Rs4/-\\ S.P.\; of\; 1\; lemon=Rs\frac { 4 }{ 5 } /-\\ S.P.\; of\; 20\; lemons=Rs\frac { 4 }{ 5 } \times 20=Rs16/-$$

Clearly, S.P.> C.P. It means girl makes Profit.

$$Profit=S.P.–C.P.\\ Profit=Rs.16-Rs.15\\ Profit=Rs.1/-$$

Hence, Gain in percentage

$$Profit\; percent=\left( \frac { Profit }{ C.P. } \right) \times 100 $$

$$Profit \% = ( \frac {1}{15}) \times 100\%$$

$$Profit\%=\frac{20}{3}\%$$

**Question**– How do you calculate profit and loss?

**Answer**– In order to calculate the profit and loss, you need to first add up all your income of the month. Then, add up the expenses for the month. After that, calculate the difference by subtracting the total expenses from the income. Finally, your result is the profit or loss.

**Question**– What is the formula of profit percentage?

**Answer**– The formula for the profit percentage is as follows:

You can calculate profit per cent by Profit % = 100 × Profit/Cost Price.

Similarly, the loss per cent can be calculated by using Loss % = 100 × Loss/Cost Price.

**Question**– What do CP and SP mean?

**Answer**– CP and SP are abbreviations for Cost Price and Selling Price. Cost price is the amount we pay to buy an item at which it is available. Similarly, Selling Price is the rate at which an article is sold which we abbreviate as SP.

**Question**– What is Profit and Loss Formula?

**Answer**– The formula for Profit is S.P. – C.P. If the selling price is lesser than the cost price, whatever difference you get between the two is the loss suffered. Similarly, Loss is C.P. – S.P. Always remember that you calculate profit or loss on the cost price.