Introduction to Percentages
October 8, 2022
Ratio and Proprotion
October 8, 2022About this post
Consider this problem - "A person sells x eggs and gains the selling price of y eggs. What is his profit percentage?".
This is a typical example problem on profit and loss. When an item is sold or bought, either a profit is gained or a loss is incurred. In profit and loss problems we deal with the cost price, selling price, percentages, gain, loss etc. The aim of this section is to help you solve problems of this kind. In addition to this, you will also learn to solve problems on faulty balances.
The first lesson in this topic is a brief introduction to profit and loss. We shared some formulae that will be required to tackle problems on profit and loss. The exercises contain solved question and answers on profit, loss and faulty balances. When solving exercises, we recommend you to try solving the problems on your own, that way you will understand better and you can define your own approach to solving problems on Profit and Loss.
Introduction to Profit and Loss
Cost Price (CP)
It is the price at which an article is purchased.
Selling Price (SP)
It is the price at which an article is sold.
Profit / Loss:
It is the difference between the selling price and the cost price. If the SP is greater than CP, it is Profit; and if SP is less than CP, it is Loss.
Profit = S.P - C.P
Loss = C.P - S.P
Profit%:
It is the profit computed as a percentage of CP.
Profit% = $\frac{\text{Profit}}{\text{CP}}$ x 100
CP, Profit and Loss can also be expressed in terms of
CP (1 + profit%) = SP, if there is an overall profit in the transaction
Loss%:
It is the loss computed as a percentage of CP.
Loss% = $\frac{\text{Loss}}{\text{CP}}$ x 100
CP, Profit and Loss can also be expressed in terms of
CP( 1 - loss%) = SP, if there is an overall loss in the transaction
Note:
- Loss or gain is always based on CP.
- If a person sells two articles at the same price one at a profit of X% and the other at a loss of X%, then the seller incurs a loss given by
Loss% = $\frac{X^2}{100}$
- If a person sells goods at CP but uses false weight, the profit percentage of the person is given by
Profit% = $\frac{\text{True Weight - False Weight}}{\text{False Weight}}$ x 100
