An electronics retailer marks a mechanical keyboard at 40% above its cost price and provides a discount of Rs. 80 on the marked price. If the keyboard is sold for Rs. 480, what is the cost price of the keyboard?

The correct option is Rs. 400.

Step-by-step explanation:

Step 1: Identify the given values from the problem.
Selling Price (SP) of the keyboard = Rs. 480
Discount offered on the marked price = Rs. 80
Markup percentage = 40% above the Cost Price (CP)

Step 2: Find the Marked Price (MP).
The selling price is obtained after subtracting the discount from the marked price. Therefore, the marked price is the sum of the selling price and the discount:

$\text{Marked Price (MP)}=\text{Selling Price (SP)}+\text{Discount}$

$\text{MP}=480+80=\text{Rs. 560}$

Step 3: Express the Marked Price in terms of the Cost Price (CP).
Since the retailer marked the keyboard at 40% above its cost price:

$\text{Marked Price}=\text{Cost Price}+40\%\text{of Cost Price}$

$\text{MP}=\text{CP}+0.40\text{CP}=1.40\text{CP}$

Step 4: Calculate the Cost Price (CP).
Substitute the calculated Marked Price (Rs. 560) into the equation:

$560=1.40\times \text{CP}$

$\text{CP}=\frac{560}{1.40}$

$\text{CP}=400$

Thus, the cost price of the keyboard is Rs. 400.