A retailer marks up an article 35% above its cost price and earn Rs 96 by giving 20% discount on the marked price. If he sells article at 15% discount on marked price then, find retailer’s profit on selling one article?

The correct option is 177.

Let us break down the solution step-by-step:

Step 1: Understand the relationship between Cost Price, Markup, and Marked Price.
Let the Cost Price (CP) of the article be $x$.
The retailer marks up the article by 35% above its cost price.
Therefore, the Marked Price (MP) is:
$\text{MP}=x+35\%\text{of}x=1.35x$

Step 2: Calculate the Selling Price and Profit with a 20% discount.
The retailer offers a 20% discount on the marked price.
The Selling Price (${\text{SP}}_1$) is:
${\text{SP}}_1=80\%\text{of}\text{MP}=0.80\times 1.35x=1.08x$
The profit earned is the difference between this selling price and the cost price:
$\text{Profit}={\text{SP}}_1-\text{CP}=1.08x-x=0.08x$

Step 3: Find the Cost Price and Marked Price using the given profit.
We are given that the initial profit earned is Rs 96. Therefore:
$0.08x=96$
Solving for $x$:
$x=\frac{96}{0.08}=1200$
So, the Cost Price (CP) is Rs 1200.
Now, we find the Marked Price (MP):
$\text{MP}=1.35\times 1200=1620$

Step 4: Calculate the profit if a 15% discount is offered instead.
If the retailer sells the article at a 15% discount on the marked price, the new Selling Price (${\text{SP}}_2$) will be:
${\text{SP}}_2=85\%\text{of}\text{MP}=0.85\times 1620=1377$
The new profit on selling one article is:
$\text{New Profit}={\text{SP}}_2-\text{CP}=1377-1200=177$