# Profit and Loss

For the purpose of comparison, we usually express the actual profit or loss as a percentage of cost price.

For example, a shopkeeper sold an article for Rs.60 which costs Rs.50 and another article sold for Rs.110 which cost Rs.100. In each case, the shopkeeper makes a profit of Rs.10. It seems that in both cases profit is equally gained.

But in percentage profit, we have:

Percentage Profit = $$\frac{{10}}{{50}}$$x 100% = 20%

Percentage Profit = $$\frac{{10}}{{100}}$$x 100% = 10%

Hence, in the first case he made more profit than in the 2nd case, this is a better and more accurate method for comparison.

**Example:**

A bag costing Rs.28 sold for Rs.35. Find the percentage profit.

**Solution:**

Let Cost Price = Rs.28

Selling Price = Rs.35

Profit = Selling Price – Cost Price = 35 – 28 = Rs.7

Percentage Profit = $$\frac{7}{{28}}$$ x 100% = 25%

**Example:**

A machine costing Rs.60 sold for Rs.50. Find the percentage loss.

**Solution:**

Let Cost Price = Rs.60

Sold Price = Rs.50

Loss = Cost Price – Sold Price = 60 – 50 = Rs.10

Percentage Loss = $$\frac{{10}}{{60}}$$ x 100% = $$16\frac{2}{3}$$%