A retailer marks up his goods by 130% and offers 25% discount. What will be the selling price (in ₹) if the cost price is ₹ 1600?

The correct answer is 2760.

Step-by-step explanation:

Step 1: Identify the given values
Cost Price (CP) = ₹ 1600
Markup percentage = 130%
Discount percentage = 25%

Step 2: Calculate the Marked Price (MP)
The retailer marks up the price of goods by 130% over the Cost Price.

$\text{Markup Amount}=130\%\text{of CP}$

$\text{Markup Amount}=\frac{130}{100}\times 1600=1.30\times 1600=2080$

Now, add the markup amount to the Cost Price to get the Marked Price:

$\text{Marked Price (MP)}=\text{Cost Price (CP)}+\text{Markup Amount}$

$\text{MP}=1600+2080=3680$

Alternatively, the Marked Price can be calculated directly using the formula:

$\text{MP}=\text{CP}\times (1+\frac{130}{100})=1600\times 2.30=3680$

Step 3: Calculate the Selling Price (SP)
The retailer offers a 25% discount on the Marked Price (MP).

$\text{Discount Amount}=25\%\text{of MP}$

$\text{Discount Amount}=\frac{25}{100}\times 3680=0.25\times 3680=920$

Subtract the discount amount from the Marked Price to find the Selling Price:

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

$\text{SP}=3680-920=2760$

Alternatively, calculating the Selling Price directly:

$\text{SP}=\text{MP}\times (1-\frac{25}{100})=3680\times 0.75=2760$

Thus, the selling price of the goods is ₹ 2760.