The average cost price of two articles P and Q is Rs 1350. Article P is sold at a 10\% profit, and article Q is sold at a 20\% profit. The total selling price of articles P and Q together is Rs 3120. If article Q is instead sold at a 40\% profit, what will be its selling price?

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**Solution:**

1. Let the cost prices of articles P and Q be $ x $ and $ y $ respectively.

2. Given the average cost price is Rs 1350, so:
   
   $$\frac{x + y}{2} = 1350 \implies x + y = 2700$$

3. Article P is sold at 10\% profit, so its selling price is:
   
   $$SP_P = x + 0.10x = 1.10x$$

4. Article Q is sold at 20\% profit, so its selling price is:
   
   $$SP_Q = y + 0.20y = 1.20y$$

5. Total selling price of P and Q is Rs 3120, so:
   
   $$1.10x + 1.20y = 3120$$

6. From step 2, $ y = 2700 - x $. Substitute in step 5:
   
   $$1.10x + 1.20(2700 - x) = 3120$$
   $$1.10x + 3240 - 1.20x = 3120$$
   $$-0.10x + 3240 = 3120$$
   $$-0.10x = 3120 - 3240 = -120$$
   $$x = \frac{120}{0.10} = 1200$$

7. Calculate $ y $:
   
   $$y = 2700 - 1200 = 1500$$

8. Now, if article Q is sold at 40\% profit, its selling price will be:
   
   $$SP_Q = y + 0.40y = 1.40 \times 1500 = 2100$$

**Answer:** Rs 2100

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