If the selling price of 80 articles is equal to the cost price of 100 articles, then find the gain percentage.

Question

Accepted Answer

Let the cost price (CP) of one article be $$ 	ext{Rs.} x $$.  
The cost price of 100 articles = $$ 100x $$.  
Let the selling price (SP) of one article be $$ 	ext{Rs.} y $$.  
The selling price of 80 articles = $$ 80y $$.

According to the question:  
$$
80y = 100x
$$  
$$
\frac{y}{x} = \frac{100}{80} = \frac{5}{4}
$$

This means the selling price is $$ \frac{5}{4} $$ times the cost price.

Gain percentage is calculated as:  
$$
	ext{Gain Percentage} = \left( \frac{	ext{SP} - 	ext{CP}}{	ext{CP}} ight) 	imes 100
$$  
Substituting values:  
$$
	ext{Gain Percentage} = \left( \frac{\frac{5}{4}x - x}{x} ight) 	imes 100 = \left( \frac{\frac{1}{4}}{} ight) 	imes 100 = 25\%
$$

Thus, the gain percentage is **25%**.

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