## Profit & Loss

This is an important chapter in Arithmetic which tests one's logical thinking. Data Interpretation cases involving application of basic profit & loss concepts (especially the fixed cost/variable cost structure) are also common. While the basic concepts are quite simple, different scenarios can be integrated to make the questions challenging. The examples in this chapter, which cover most question types, will prepare you for quick understanding of the question/logic, selection of the right approach and application of the same.

### 1. Cost Price, Selling Price & Profit

The Selling Price (SP) is the price at which a good or commodity is sold.

The Cost Price (CP) is the price at which the good or commodity is purchased.

Typically, one purchases at a lower price and sells at a higher price to make a profit. The amount by which the Selling Price exceeds the Cost Price is called Profit.

Profit = SP - CP
$\implies$ SP = CP + Profit
$\implies$ CP = SP - Profit

∴ If any two of SP, CP or Profit are known, the third can be computed.

When CP is more than SP, profit is negative. This is called a Loss.
(Note: Loss is written as a positive value. So, profit of $- 5000$ is a loss of $5,000$)

### Example 1

If the cost price of an item was Rs. $450$ and the shopkeeper made a profit of $10 \%$ when he sold it, what price did he sell it at?

### Solution

Profit is a percentage of the Cost Price (or purchase price).

Profit $= \dfrac{10}{100} \times 450 = \text{Rs.} 45$

Selling Price $=$ Cost Price + Profit $= 450 + 45 =$ Rs. $495$

Answer: $495$