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).

To find the cost price of the article, we can set up the relationships between the Cost Price (CP), Marked Price (MP), and Selling Price (SP) step-by-step.

Let the cost price of the article be $\mathrm{CP}$ (in Rs).

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

$\mathrm{MP}=\mathrm{CP}+80\%\text{of}\mathrm{CP}$

$\mathrm{MP}=\mathrm{CP}+0.8\mathrm{CP}=1.8\mathrm{CP}$

Step 2: Determine the Selling Price (SP)
A discount of Rs 160 is given on the marked price. The selling price is calculated as:

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

$\mathrm{SP}=1.8\mathrm{CP}-160$

Step 3: Relate Selling Price to Profit
The profit obtained is Rs 200. Profit is the difference between the selling price and the cost price:

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

Substituting the values we know into this equation:

$200=(1.8\mathrm{CP}-160)-\mathrm{CP}$

Step 4: Solve for the Cost Price (CP)
Simplify the right side of the equation:

$200=0.8\mathrm{CP}-160$

Add 160 to both sides of the equation:

$0.8\mathrm{CP}=200+160$

$0.8\mathrm{CP}=360$

Divide both sides by 0.8:

$\mathrm{CP}=\frac{360}{0.8}$

$\mathrm{CP}=450$

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