A shopkeeper marked up the price of article P by 20% and give discount of d%, then he gets a loss of (d – 11) %. If cost price of article Q is Rs.200 and gets a profit of 1.5d%, then find the selling price of the article Q.

The correct option is Rs.335.

Let's solve the problem step-by-step to find the selling price of article Q.

Step 1: Understand the relations for Article P
Let the Cost Price (CP) of article P be 100 units.
The shopkeeper marks up the price of article P by 20%.
Therefore, Marked Price (MP) of article P = $100+20=120$ units.

A discount of d% is given on the Marked Price.
Selling Price (SP) of article P = $120\times (1-\frac{d}{100})$ units.

He incurs a loss of (d – 11)%.
Selling Price (SP) of article P in terms of CP and loss percentage = $100\times (1-\frac{d-11}{100})$ units.

Step 2: Equate the two expressions for the Selling Price of article P

$120\times (1-\frac{d}{100})=100\times (1-\frac{d-11}{100})$

Expanding both sides:
$120-1.2d=100-(d-11)$

$120-1.2d=100-d+11$

$120-1.2d=111-d$

Rearranging terms to solve for d:
$120-111=1.2d-d$

$9=0.2d$

$d=\frac{9}{0.2}=45$

Step 3: Calculate the Selling Price of Article Q
The cost price of article Q is given as Rs.200.
The profit percentage on article Q is $1.5d\%$.

Substitute $d=45$ into the profit percentage formula:
Profit percentage = $1.5\times 45\%=67.5\%$

Now, compute the Selling Price of article Q:
Selling Price = $\text{CP}\times (1+\frac{\text{Profit \%}}{100})$

$\text{Selling Price}=200\times (1+\frac{67.5}{100})$

$\text{Selling Price}=200\times 1.675=\text{Rs.335}$

Hence, the selling price of article Q is Rs.335.