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.

Correct Option: The correct answer is 2100 Rs.

Let us solve this problem step-by-step.

Step 1: Find the total cost price of articles P and Q.
We are given that the average cost price (CP) of two articles P and Q is Rs 1350.
Therefore, the total cost price of P and Q is:
$\text{Total CP}=1350\times 2=2700\text{Rs}$

Let the cost price of article P be ${\mathrm{CP}}_P$ and the cost price of article Q be ${\mathrm{CP}}_Q$.
So, we have:
${\mathrm{CP}}_P+{\mathrm{CP}}_Q=2700$          — (Equation 1)

Step 2: Use the selling price information to form a second equation.
Article P is sold at a 10% profit, and article Q is sold at a 20% profit. The total selling price (SP) of P and Q is Rs 3120.
The total profit earned on both articles is:
$\text{Total Profit}=\text{Total SP}-\text{Total CP}$
$\text{Total Profit}=3120-2700=420\text{Rs}$

Since the profit on article P is 10% of its cost price, and the profit on article Q is 20% of its cost price, we can write:
$10\%\text{of}{\mathrm{CP}}_P+20\%\text{of}{\mathrm{CP}}_Q=420$
$0.10{\mathrm{CP}}_P+0.20{\mathrm{CP}}_Q=420$

Multiply the entire equation by 10 to simplify:
${\mathrm{CP}}_P+2{\mathrm{CP}}_Q=4200$          — (Equation 2)

Step 3: Solve for the cost price of article Q.
Subtract Equation 1 from Equation 2:
$({\mathrm{CP}}_P+2{\mathrm{CP}}_Q)-({\mathrm{CP}}_P+{\mathrm{CP}}_Q)=4200-2700$
${\mathrm{CP}}_Q=1500\text{Rs}$

Step 4: Find the selling price of article Q at 40% profit.
If article Q is sold at a 40% profit, the selling price will be:
$\text{Selling Price}={\mathrm{CP}}_Q\times (1+0.40)$
$\text{Selling Price}=1500\times 1.40=2100\text{Rs}$