# 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% = $16\frac{2}{3}$%