## Profit and Loss

Theory

Profit and loss is one of the easiest topics in the Quantitative Aptitude section. Every year, one or two questions will be asked in the examination. Most of these questions can be solved easily by applying formulae. Below are some of the formulae that will help in solving these questions in the least possible time.

Theory

Cost Price (CP):
The price at which an article is bought is called the Cost Price of the article.

Selling Price (SP):
The price at which an article is sold is called the Selling Price of the article.

Marked Price (MP or MRP):
The price at which an article is marked or labelled is called the Marked Price of the article.

Profit or Gain:
The difference between the Cost Price and the Selling Price of an article where the Selling Price is greater than its Cost Price is called its Profit or Gain.

Loss:
The difference between the Cost Price and the Selling Price of an article where the Cost Price is greater than its Selling Price is called its Loss.

Discount:
The difference between the Marked Price and the Selling Price of an article is called its Discount.

Formula
1. Profit = Selling Price - Cost Price
2. Profit Percentage = $$\dfrac{Profit}{\text{Cost Price}}\times100 = \dfrac{\text{Selling Price - Cost Price}}{\text{Cost Price}}\times100$$
3. Loss = Cost Price - Selling Price
4. Loss Percentage = $$\dfrac{Loss}{\text{Cost Price}}\times100 = \dfrac{\text{Cost Price - Selling Price}}{\text{Cost Price}}\times100$$
5. Discount = Marked Price - Selling Price
6. Discount Percentage = $$\dfrac{Discount}{\text{Marked Price}}\times100 = \dfrac{\text{Marked Price - Selling Price}}{\text{Marked Price}}\times100$$

7. Cost Price when Selling Price and Profit are given:
Cost Price = $$\dfrac{100}{100+Profit}\times\text{Selling Price}$$
8. Selling Price when Cost Price and Profit are given:
Selling Price = $$\dfrac{100+Profit}{100}\times\text{Cost Price}$$
9. Cost Price when Selling Price and Loss are given:
Cost Price = $$\dfrac{100}{100-Loss}\times\text{Selling Price}$$
10. Selling Price when Cost Price and Loss are given:
Selling Price = $$\dfrac{100-Loss}{100}\times\text{Cost Price}$$
11. If a trader uses false weight, then profit earned = $$\dfrac{Error}{\text{True Value - Error}}\times100$$
Solved Example

Q) Find the profit percentage obtained on an article if it is bought at Rs.250 and sold at Rs.360.

Solution: Given, Cost Price = Rs.250
Selling Price = Rs.360

Profit = Rs.360 - Rs.250 = Rs.110.

Profit percentage = 110/250*100 = 44%.

Solved Example

Q) Find the loss percentage on an article if it is bought at Rs.520 and sold at Rs.480.

Solution: Given, Cost Price = Rs.520.
Selling Price = Rs.480.

Loss = Rs.520 - Rs.480 = Rs.40.

Loss percentage = 40/520*100 = 7.69%

Solved Example

Q) Find the Selling Price of the article when an article is bought at Rs.1000 and was marked 10% above its cost price and given a discount of 10%.

Solution:

Cost Price of the article = Rs.1000

Marked price is 10% above Rs.1000 = 110% of 1000 = Rs.1100.

Discount = 10% of 1100 = Rs,110

Selling price = Rs.1100 - Rs.110 = Rs,990.

Shortcuts

Effective discount when two successive discounts of x% and y% are given = $$x+y-\dfrac{xy}{100}$$

Solved Example

Q) Find the Selling Price of an article which is marked at Rs.1000 and was given two successive discounts of 10% and 15%.

Solution:
Marked Price of the article = Rs.1000
Effective discount percentage = $$10+15-\dfrac{10\times15}{100} = 25-1.5 = 23.5$$%.

Discount = 23.5% of 1000 = Rs.235.

Selling Price = Rs.1000 - Rs.235 = Rs.765.