Explanation:

Let's break it down:

- A's investment is Rs. 15000 for 12 months.

- B's initial investment is Rs. (15000 + Y) for 4 months.

- After 4 months, B withdraws 40% of his investment. So, B remains with 60% of his investment for the remaining 8 months.

- Considering the investment time, the effective investment by B:

- For the first 4 months: Rs. (15000 + Y)

- For the remaining 8 months: Rs. 0.6 * (15000 + Y)

- Total profit is Rs. 4700, with B's share being Rs. 2200.

- Profit sharing is proportional to the investment time:

$$

\begin{align*}

\text{A's ratio of profit} &= 15000 \times 12 \\

\text{B's ratio of profit} &= (15000 + Y) \times 4 + (15000 + Y) \times 8 \times 0.6 \\

\text{Ratio of A to B} &= \dfrac{2500}{2200}

\end{align*}

$$

- Equate B's profit share to his investment time ratio:

$$

\begin{align*}

4700 - 2200 &= \dfrac{15000 \times 12}{(15000 + Y) \times 4 + (15000 + Y) \times 8 \times 0.6} \times 2200

\end{align*}

$$

- Solving gives you the value of Y:

$$

13000Y = 1500000 \quad \Rightarrow \quad Y = \frac{1500000}{13000} = \frac{210000}{23}

$$

- Correct option is:

$$

\text{Option 1: } \quad \boxed{\textcolor{green}{210000/23 \, \, \, \textcolor{green}{\large \checkmark}}}

$$