Explanation:

Let’s walk through this problem clearly, bullet by bullet:

- Let’s call A’s investment = x.

- That means B invests 2x, and since B = 3C, C’s investment is (2x/3).

- Invested time ratios: A:B:C = 1:2:3. So Time_A = t, Time_B = 2t, Time_C = 3t.

- Their shares in profit are calculated as (Investment × Time):

- A: x × t

- B: 2x × 2t = 4xt

- C: (2x/3) × 3t = 2xt

- Combined investment ratios: A:B:C = xt : 4xt : 2xt = 1 : 4 : 2

- Total parts = 1 + 4 + 2 = 7

- Difference between C and A’s profit = C’s share – A’s share = (2/7) – (1/7) = (1/7) of total profit = Rs 1410

- So, (1/7) of profit = 1410

- Total profit = 1410 × 7 = Rs 9870

- Option 3 is correct.

Correct answer: Option 3 — Rs 9870

The options break down like this:

- Option 1, 2, 4, 5: Calculating (1/7) of these values wouldn’t give Rs 1410 difference.

- Option 3 works because (1/7) × 9870 = Rs 1410.

That’s how it all fits together, plain and simple.