Overview

Cost Price (CP) - This is the price at which an article is purchased.
Selling price (SP) - This is the price at which an article is sold.

Profit (P) - If the selling price exceeds the cost price (i.e. SP > CP), then there is profit.
Profit = SP – CP

Loss (L) - If the selling price of an article is less than its cost price (i.e. SP < CP), then there is loss.
Loss = CP – SP

Profit/Loss percent

Percentage profit and percentage loss are always calculated on cost price (C.P.) unless otherwise stated (i.e. C.P. is the base).

Profit percent

Profit percent = ($\frac{Profit}{CP}$) × 100

Now, SP = CP + Profit = CP + $\frac{CP × Profit \hspace{1ex} percent}{100}$ = ($\frac{100 + Profit \hspace{1ex} percent}{100}$) × CP

OR, CP = ($\frac{100}{100 + Profit \hspace{1ex} percent}$) × SP

Loss percent

Similarly, Loss percent = ($\frac{Loss}{CP}$) × 100

Now, SP = CP - Loss = CP - $\frac{CP × Loss \hspace{1ex} percent}{100}$ = ($\frac{100 - Loss \hspace{1ex} percent}{100}$) × CP

OR, CP = ($\frac{100}{100 - Loss \hspace{1ex} percent}$) × SP

Multiplying Factor

We saw that:
SP = ($\frac{100 + Profit \hspace{1ex} percent}{100}$) × CP OR ($\frac{100 - Loss \hspace{1ex} percent}{100}$) × CP

So, basically we have a relation SP = CP × Multiplying Factor (MF)

The MF is:

• greater than 1 in case of a profit and
• less than 1 in case of loss.

We can also write the expression as:
MF = $\frac{SP}{CP}$

From this multiplying factor, one can easily deduce the profit or loss percentage.

E.g. If CP = 16 and SP = 20, then:
MF = $\frac{SP}{CP}$ = $\frac{20}{16}$ = $\frac{5}{4}$ = 1.25, i.e. a profit percentage of 25%.

Q. Ajay bought a book for Rs. 50 and sold it for Rs. 60. What it his profit percentage?

Explanations :
1 2 3

Q. If a pen is sold for Rs. 24, there is a loss of 20%. What was the cost price of the pen?

(a) Rs. 30         (b) Rs. 40          (c) Rs. 36          (d) Rs. 20

Explanations :
1 2 3 4