A man sells two articles for ₹3600 each. He makes a profit of 20% on the first but a loss of 10% on the second. What will be his total profit percentage (%)?

Correct option is A

Given:

A man sells two articles for ₹3600 each.

He makes a profit of 20% on the first but a loss of 10% on the second. 

Formula used:

$$\text{Profit} = \frac{\text{Profit Percentage}}{100} \times \text{Cost Price}$$

$$\text{Loss} = \frac{\text{Loss Percentage}}{100} \times \text{Cost Price}$$

$$\text{Cost Price} = \frac{\text{Selling Price}}{1 + \frac{\text{Profit Percentage}}{100}} \quad \text{(for profit)}$$

$$\text{Cost Price} = \frac{\text{Selling Price}}{1 - \frac{\text{Loss Percentage}}{100}} \quad \text{(for loss)}$$​​​​​

Solution:

For the first article (Profit):

​$$\text{Cost Price}_1 = \frac{3600}{1 + \frac{20}{100}}$$​​

​$$\text{Cost Price}_1 = \frac{3600}{1 + 0.2}$$​​

​$$\text{Cost Price}_1= \frac{3600}{1.2}$$​​

$$\text{Cost Price}_1 = 3000$$

For the second article (Loss):

$$\text{Cost Price}_2 = \frac{3600}{1 - \frac{10}{100}}$$​

​$$\text{Cost Price}_2 = \frac{3600}{1 -0.1}$$​​

​$$\text{Cost Price}_2 = \frac{3600}{0.9}$$​

​$$\text{Cost Price}_2 = 4000​​$$

Total Cost Price = 3000 + 4000

Total Cost Price = 7000

Total Selling Price = 3600 + 3600

Total Selling Price = 7200

Total Profit=Total Selling Price−Total Cost Price
Total Profit = 7200 − 7000 = 200

Profit Percentage = $$\left( \frac{200}{7000} \right) \times 100$$​

Profit Percentage = 2.86%

So, 2.86% will be his total profit percentage (%).

Thus, the correct answer is (a).

Alternative method:

Profit =  5x : 6x

Loss =  10y : 9y

Equal selling price in both ratio,

Profit =  15z : 18z

Loss =  20z: 18z

18z = 3600

z = 200

Now cost price of both,

15z =  3000

20z =  4000 

Total Cost Price = 7000

Total Profit = 7200 − 7000 = 200

Profit Percentage = $$\left( \frac{200}{7000} \right) \times 100$$

Profit Percentage = 2.86%​​