Profit and Loss

The producerproduces a goods at some certain cost. When those goods are sold at a higher price than the production price, then there is profit. And, if the goods are sold at lower price than production cost, then he suffers a loss.

Thus, profit = Selling price - Cost price

or,Profit = S.P - C.P

Loss = Cost Price - Selling Price

or, Loss= C.P - S.P

For example:

If Renu bought a book for Rs 500 and sold it for Rs 600, then she made a profit of Rs 100 i.e profit = Rs 100

Similarly, if Ritesh bought a machine for Rs 200 and sold it for Rs 100, then he suffered a loss of Rs 100. i.e loss = Rs 200 - Rs 100 = Rs 100 (loss)

Profit Percentage and Loss Percentage

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

For example; Samikshya sold a bag for Rs 60 which costs Rs 50 and shoes sold for Rs 110 which costs 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 we have:

In the first case, profit percentage = \(\frac{10}{ 50}\) x 100 = 20 %

In the second case, profit percent = \(\frac{10}{100}\) x 100 = 10 %

Hence, in the first case, she made more profit than in the second case, it is better and accurate method of comparison.

Have a look at these formulas:

Percentage profit = \(\frac{actual\;profit}{C.P}\) x 100

Percentage loss = \(\frac{actual\;loss}{C.P}\) x 100

Examples

1. A pen costing Rs 28 sold for RS 36. Find the percentage profit.
   Solution:
   Cost price (CP) = RS 28
   Selling price(SP) = Rs 35
   Actual profit = SP - CP = Rs 35 - Rs 28 = Rs 7
   Percentage profit= \(\frac{actual \;profit}{CP}\)×100 =\(\frac{7}{28}\)×100 =25%
   
   
2. A book costing Rs 60 sold for Rs 50. Find the percentage loss.
   Solution:
   Cost price (CP) = Rs 60
   Selling price (SP) = Rs 50
   Actual loss = CP - SP = Rs 60 - Rs 50 = Rs 10
   Percentage loss = \(\frac{actual \;loss}{CP}\)×100 =\(\frac{10}{60}\)×100 =16\(\frac{2}{3}\)%