Two teams named A and B do business together and their shares are in the ratio of 2 : 1. Team A has got three members A₁, A₂ and A₃ whose shares are in the ratio of 1 : 2 : 3. Team B has got four members B₁, B₂, B₃ and B₄ whose shares are in the ratio of 1 : 2 : 3 : 4. If the actual share of B₃ is ₹ 2,25,000, then what is the actual share of A₂ ?

To find the share of A₂, we follow these steps based on the given ratios:

1. Calculate Team B's total share: The ratio for B₁:B₂:B₃:B₄ is 1:2:3:4. The sum of parts is 1 + 2 + 3 + 4 = 10. Since B₃'s share (3 parts) is ₹ 2,25,000, one part equals 2,25,000 ÷ 3 = ₹ 75,000. Thus, Team B's total share = 10 × 75,000 = ₹ 7,50,000.
2. Calculate Team A's total share: The ratio of shares between Team A and Team B is 2 : 1. Therefore, Team A's total share = 2 × 7,50,000 = ₹ 15,00,000.
3. Calculate A₂'s share: The ratio for A₁:A₂:A₃ is 1:2:3. The sum of parts is 1 + 2 + 3 = 6. A₂'s share is 2/6 (or 1/3) of Team A's total share.
4. A₂'s share = (1/3) × 15,00,000 = ₹ 5,00,000.

Thus, the correct option is A.