The average cost price of two articles P and Q is Rs 1350. Article P sold at 10% profit and article Q sold at 20% profit. The total selling price of article P and Q is Rs 3120. If article Q is sold at 40% profit, then find the selling price.

To find the selling price of article Q when sold at a 40% profit, we will determine the cost price of both articles step-by-step.

Step 1: Understand the given values and set up equations.
Let the cost price of article P be _$P$ and the cost price of article Q be _$Q$.
We are given that the average cost price of the two articles is Rs 1350:
$\frac{P+Q}{2}=1350$
Multiplying by 2, we get the total cost price of both articles:
$P+Q=2700$      --- (Equation 1)

Step 2: Use the selling price information.
Article P is sold at a 10% profit, so its selling price is:
$1.1P$
Article Q is sold at a 20% profit, so its selling price is:
$1.2Q$
The total selling price of both articles is Rs 3120:
$1.1P+1.2Q=3120$      --- (Equation 2)

Step 3: Solve the system of equations.
Multiply Equation 1 by 1.1 to align the coefficients:
$1.1P+1.1Q=1.1\times 2700$
$1.1P+1.1Q=2970$      --- (Equation 3)
Now, subtract Equation 3 from Equation 2:
$(1.1P+1.2Q)-(1.1P+1.1Q)=3120-2970$
$0.1Q=150$
Multiplying by 10 gives the cost price of article Q:
$Q=1500$ Rs

Step 4: Calculate the selling price of Q at a 40% profit.
If article Q is sold at a 40% profit, the new selling price is:
$\text{Selling Price}=Q\times (1+0.40)$
$\text{Selling Price}=1500\times 1.4$
$\text{Selling Price}=2100$ Rs

Thus, the selling price of article Q when sold at a 40% profit is 2100 Rs.