A mark up the good 80% above the cost price and give a discount of Rs 160. If he gets a profit of Rs 200, the find the cost price of the article (in Rs).

The correct option is 450.

To find the cost price of the article, we can break down the problem into simple algebraic steps by setting up an equation for the profit.

Let the Cost Price (CP) of the article be:

$x$

rupees.

Step 1: Determine the Marked Price (MP)
The article is marked up by 80% above the cost price.
The markup amount is:

$80\%\text{of}x=0.8x$

Therefore, the Marked Price (MP) is CP plus the markup amount:

$\text{MP}=x+0.8x=1.8x$

Step 2: Determine the Selling Price (SP)
A discount of Rs 160 is given on the Marked Price. Thus, the Selling Price is:

$\text{SP}=\text{MP}-160$

Substituting the expression for MP from Step 1:

$\text{SP}=1.8x-160$

Step 3: Relate Selling Price to Profit
We are given that the profit obtained is Rs 200. Profit is defined as Selling Price minus Cost Price:

$\text{Profit}=\text{SP}-\text{CP}$

Substituting the known values into the profit formula:

$200=(1.8x-160)-x$

Step 4: Solve for the Cost Price ($x$)
Combine the terms containing $x$ on the right-hand side:

$200=0.8x-160$

Add 160 to both sides of the equation to isolate the term with $x$:

$200+160=0.8x$

$360=0.8x$

Now, divide both sides by 0.8 to solve for $x$:

$x=\frac{360}{0.8}$

$x=450$

Therefore, the cost price of the article is Rs 450.