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.

The correct option is 2100 Rs.

To find the selling price of article Q when sold at 40% profit, we can break down the problem into step-by-step calculations:

Step 1: Understand the Cost Prices (CP)
Let the cost price of article P be ${\mathrm{CP}}_P$ and the cost price of article Q be ${\mathrm{CP}}_Q$.
We are given that the average cost price of the two articles is Rs 1350. Therefore:

$\frac{{\mathrm{CP}}_P+{\mathrm{CP}}_Q}{2}=1350$

Multiplying both sides by 2, we get the sum of the cost prices of P and Q:
${\mathrm{CP}}_P+{\mathrm{CP}}_Q=2700$ ---- (Equation 1)

Step 2: Formulate the Selling Prices (SP)
Article P is sold at a 10% profit, which means its selling price is:
${\mathrm{SP}}_P=1.10\times {\mathrm{CP}}_P$
Article Q is sold at a 20% profit, which means its selling price is:
${\mathrm{SP}}_Q=1.20\times {\mathrm{CP}}_Q$

We are given that the total selling price of both articles is Rs 3120:
$1.10{\mathrm{CP}}_P+1.20{\mathrm{CP}}_Q=3120$ ---- (Equation 2)

Step 3: Solve for the Cost Price of Article Q (${\mathrm{CP}}_Q$)
To eliminate ${\mathrm{CP}}_P$, we can multiply Equation 1 by 1.10:

$1.10{\mathrm{CP}}_P+1.10{\mathrm{CP}}_Q=1.10\times 2700$

$1.10{\mathrm{CP}}_P+1.10{\mathrm{CP}}_Q=2970$ ---- (Equation 3)

Now, subtract Equation 3 from Equation 2:
$(1.20{\mathrm{CP}}_Q-1.10{\mathrm{CP}}_Q)=3120-2970$

$0.10{\mathrm{CP}}_Q=150$

Dividing both sides by 0.10, we find the cost price of article Q:
${\mathrm{CP}}_Q=1500$ Rs

Step 4: Find the Selling Price of Q at 40% Profit
If article Q is sold at a 40% profit, the new selling price of Q is calculated as:
$\mathrm{New}{\mathrm{SP}}_Q={\mathrm{CP}}_Q\times (1+0.40)$

$\mathrm{New}{\mathrm{SP}}_Q=1500\times 1.40=2100$ Rs

Thus, the required selling price of article Q is 2100 Rs.