To solve this problem, we need to calculate the ratio of the investments made by P, Q, and R initially.
Let's calculate the ratio of their investments:
P's investment = Rs. 20000
Q's investment = Rs. 30000
R's investment = Rs. 40000
To calculate the ratio, we divide each investment by the total investment:
Total investment = Rs. (20000 + 30000 + 40000) = Rs. 90000
P's ratio = Rs. 20000 / Rs. 90000 = 2/9
Q's ratio = Rs. 30000 / Rs. 90000 = 3/9 = 1/3
R's ratio = Rs. 40000 / Rs. 90000 = 4/9
Now, let's calculate the time for which each partner remains in the partnership:
P remains in the partnership for 2 months.
Q remains in the partnership for 4 months.
R remains in the partnership for 8 months.
To calculate the share of each partner, we multiply their ratios with their respective time periods:
P's share = (2/9) * 2 = 4/9
Q's share = (1/3) * 4 = 4/9
R's share = (4/9) * 8 = 32/9
Now, let's calculate the total share of R:
Total share of R = R's share / (P's share + Q's share + R's share) * Total Profit
Total share of R = (32/9) / (4/9 + 4/9 + 32/9) * Rs. 12474
Total share of R = (32/9) / (40/9) * Rs. 12474
Total share of R = (8/40) * Rs. 12474
Total share of R = (1/5) * Rs. 12474
Total share of R = Rs. 2494.8
Therefore, R's share in the profit of Rs. 12474 is approximately Rs. 2494.8.
Since none of the given options match this value exactly, there might be a mistake in the question or the answer choices provided.