Explanation:

- To solve the problem, let's denote the cost price of the painting as \( CP \).

- When the painting is sold for Rs1,200, the profit is \( 1,200 - CP \).

- When sold for Rs240, the loss is \( CP - 240 \).

- According to the problem, the profit is 15 times the loss:

$$

1,200 - CP = 15 \times (CP - 240)

$$

- Solving the equation:

$$

1,200 - CP = 15CP - 3,600

$$

$$

4,800 = 16CP

$$

$$

CP = 300

$$

- To find the selling price for a 40% profit:

$$

\text{Selling price} = CP \times 1.40 = 300 \times 1.40 = 420

$$

- The correct option is option 3: Rs420.