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.

Let us solve the problem step-by-step to find the selling price of article Q when it is sold at a 40% profit.

Step 1: Find the total cost price of articles P and Q.

We are given that the average cost price of articles P and Q is Rs 1350.
Let ${\mathrm{CP}}_{\mathrm{P}}$ be the cost price of article P and ${\mathrm{CP}}_{\mathrm{Q}}$ be the cost price of article Q.

$\frac{{\mathrm{CP}}_{\mathrm{P}}+{\mathrm{CP}}_{\mathrm{Q}}}{2}=1350$

${\mathrm{CP}}_{\mathrm{P}}+{\mathrm{CP}}_{\mathrm{Q}}=1350\times 2=2700$    --- (Equation 1)

Step 2: Express the total selling price in terms of cost prices.

Article P is sold at a 10% profit, so its selling price is:
${\mathrm{SP}}_{\mathrm{P}}=1.10\times {\mathrm{CP}}_{\mathrm{P}}$

Article Q is sold at a 20% profit, so its selling price is:
${\mathrm{SP}}_{\mathrm{Q}}=1.20\times {\mathrm{CP}}_{\mathrm{Q}}$

The total selling price of both articles is given as Rs 3120.

$1.10{\mathrm{CP}}_{\mathrm{P}}+1.20{\mathrm{CP}}_{\mathrm{Q}}=3120$    --- (Equation 2)

Step 3: Solve Equations 1 and 2 to find the cost price of article Q.

From Equation 1, we can write:
${\mathrm{CP}}_{\mathrm{P}}=2700-{\mathrm{CP}}_{\mathrm{Q}}$

Substitute ${\mathrm{CP}}_{\mathrm{P}}$ into Equation 2:

$1.10(2700-{\mathrm{CP}}_{\mathrm{Q}})+1.20{\mathrm{CP}}_{\mathrm{Q}}=3120$

$2970-1.10{\mathrm{CP}}_{\mathrm{Q}}+1.20{\mathrm{CP}}_{\mathrm{Q}}=3120$

$2970+0.10{\mathrm{CP}}_{\mathrm{Q}}=3120$

$0.10{\mathrm{CP}}_{\mathrm{Q}}=3120-2970$

$0.10{\mathrm{CP}}_{\mathrm{Q}}=150$

${\mathrm{CP}}_{\mathrm{Q}}=\frac{150}{0.10}=1500$

Thus, the cost price of article Q is Rs 1500.

Step 4: Find the selling price of article Q if sold at a 40% profit.

With a 40% profit margin, the new selling price of article Q will be:

${\mathrm{New\; SP}}_{\mathrm{Q}}={\mathrm{CP}}_{\mathrm{Q}}\times (1+\frac{40}{100})$

${\mathrm{New\; SP}}_{\mathrm{Q}}=1500\times 1.40=2100$

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