A profit of 10% is made when a smartphone is sold at P rupees and there is 4% loss when the smartphone is sold at Q rupees. Then P ∶ Q is

Concept:

Profit = Selling Price - Cost Price

Loss = Cost Price - Selling Price

Calculation:

Let the cost price of smartphone = x rupees

Now, Profit = Selling Price - Cost Price

⇒ 10% of x = P - x

⇒ \(\frac{x}{10}\) = P - x

⇒ \(\frac{x}{10}\) + x = P

⇒ P = \(\frac{11x}{10}\)

Also, Loss = Cost Price - Selling Price

⇒ 4% of x = x - Q

⇒ \(\frac{4x}{100}\) = x - Q

⇒ \(\frac{x}{25}\) = x - Q

⇒ Q = x - \(\frac{x}{25}\)

⇒ Q = \(\frac{24x}{25}\)

∴ P ∶ Q = \(\displaystyle \frac{\frac{11x}{10}}{\frac{24x}{25}}\) = \(\frac{11}{10}\times\frac{25}{24}\) = 55 ∶ 48 

∴ P ∶ Q = 55 ∶ 48 = 110 ∶ 96