**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:

- Profit = Selling Price – Cost Price
- Loss = Cost Price – Selling Price
- Cost Price = Selling Price – Profit or, Selling Price + Loss
- Selling Price = Cost Price + Profit or, Cost Price – Loss
- 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

- A cloth merchant on selling of cloth obtains a profit equal to the selling price of of cloth. Find his profit per cent.
- 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.
- 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 ?
- By selling bananas, a vendor loses the selling price of bananas. Find his loss per cent.
- 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 ?

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