The cash difference between the selling prices of an article at a profit of 8% and at a loss of 4% is ₹54. Find the cost price of the article.

Let's assume the cost price of the article is 100y.

The cash difference between the selling prices of an article at a profit of 8% and at a loss of 4% is ₹54.

selling price of an article when profit = 100y of (100+8)%

= 100y of 108%

= $$100y\times\frac{108}{100}$$

= 108y    Eq.(i)

selling price of an article when loss = 100y of (100-4)%

= 100y of 96%

= $$100y\times\frac{96}{100}$$

= 96y    Eq.(ii)

So Eq.(i)- Eq.(ii) = 108y-96y = ₹54

12y = ₹54

y = $$\frac{54}{12}$$

y = 4.5

Cost price of the article = 100y

= $$100\times4.5$$

= ₹450