The mean cost price of two products, A and B, is Rs 2500. Product A is sold at a profit of 20%, and product B is sold at a profit of 30%. The combined selling price of both products is Rs 6300. If product B is sold at a 40% profit, find the new selling price of product B (in Rs).

The correct answer is 4200.

Step 1: Calculate the total cost price of products A and B.
The mean cost price of products A and B is Rs 2500.

$\text{Total Cost Price}={\mathrm{CP}}_A+{\mathrm{CP}}_B=2500\times 2=5000$

Therefore, we get equation (1):

${\mathrm{CP}}_A+{\mathrm{CP}}_B=5000$

Step 2: Formulate the equation for the combined selling price.
Product A is sold at a 20% profit, so its selling price is:

${\mathrm{SP}}_A=1.20\times {\mathrm{CP}}_A$

Product B is sold at a 30% profit, so its selling price is:

${\mathrm{SP}}_B=1.30\times {\mathrm{CP}}_B$

The combined selling price is given as Rs 6300. Thus:

$1.20\times {\mathrm{CP}}_A+1.30\times {\mathrm{CP}}_B=6300$

Step 3: Solve for the cost price of product B.
From equation (1), substitute ${\mathrm{CP}}_A=5000-{\mathrm{CP}}_B$ into the combined selling price equation:

$1.20\times (5000-{\mathrm{CP}}_B)+1.30\times {\mathrm{CP}}_B=6300$

$6000-1.20\times {\mathrm{CP}}_B+1.30\times {\mathrm{CP}}_B=6300$

$6000+0.10\times {\mathrm{CP}}_B=6300$

$0.10\times {\mathrm{CP}}_B=6300-6000$

$0.10\times {\mathrm{CP}}_B=300$

${\mathrm{CP}}_B=\frac{300}{0.10}=3000$

So, the cost price of product B is Rs 3000.

Step 4: Find the new selling price of product B at a 40% profit.
If product B is sold at a 40% profit, the new selling price is:

$\text{New}{\mathrm{SP}}_B={\mathrm{CP}}_B\times (1+0.40)$

$\text{New}{\mathrm{SP}}_B=3000\times 1.40=4200$

Thus, the new selling price of product B is Rs 4200.