A man sells an article at a certain price. If on selling it at 75% of that price, he loses 10%, what is his profit or loss percentage in the initial selling price?

Correct option is D

Given: 

A man sells an article at a certain price. If on selling it at 75% of that price, he loses 10%

Formula Used:

​$$\text{Loss\%} = \left( \frac{\text{Cost Price} - \text{Selling Price}}{\text{Cost Price}} \right) \times 100$$ 

$$\text{Profit\%} = \left( \frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \right) \times 100$$​​

Solution:

Let cost price of the article be = Rs.100x and selling price of article = Rs.100y
When sold at 75% of the price, new selling price = Rs. 75y
​$$\text{Loss\%} = \left( \frac{100x - 75y}{100x} \right) \times 100\\\Rightarrow 10 = \frac{100x - 75y}{x}\\\Rightarrow 90x = 75y\\\Rightarrow \frac{x}{y} = \frac{75}{90} = \frac{5}{6}\\$$​​
So, x = 5, y = 6
CP = 500, SP = 600
Profit % = $$\frac{600 - 500}{500}$$​× 100 = 20%
∴ Profit % is 20%​​

Alternate Solution:
Let the price at which shopkeeper sell the article = 100
If he sold at 75% of 100 he losses 10%
75% of 100 = 75
75 is 90% of the cost price
=> 90% = 75
​$$\Rightarrow 1\% = \frac{75}{90} \\\Rightarrow 100\% = \left( \frac{75}{90} \right) \times 100 = \frac{250}{3}\\ \\\text{Cost price} = \frac{250}{3} \\$$​​
As we assumed selling price = 100
​$$\text{Profit} = 100 - \left( \frac{250}{3} \right) = \frac{50}{3} \\\Rightarrow \text{Profit\%} = \left[ \frac{\frac{50}{3}}{\frac{250}{3}} \right] \times 100 = \left[ \frac{50}{250} \right] \times 100 = 20\%$$​​