At a casino in Mumbai, there are 3 tables A, B and C. The pay offs at A is 10:1 at B is 20:1 and at C is 30:1.If a man bets Rs. 200 at each table and with at two of the tables, what is the maximum and minimum difference between his earnings can be?

Options

A. Rs. 2500
B. Rs. 2000
C. Rs. 4000
D. None of these

Answer

To solve the problem, we need to calculate the maximum and minimum difference between the earnings of a man who bets Rs. 200 at each of the three tables (A, B, and C) with different payoffs.

### Step-by-Step Solution:

1. **Understanding the Payoffs**:
- Table A: Payoff is 10:1
- Table B: Payoff is 20:1
- Table C: Payoff is 30:1

2. **Calculating Potential Earnings**:
- If the man bets Rs. 200 at each table:
- If he wins at Table A: Earnings = 10 * Rs. 200 = Rs. 2000
- If he wins at Table B: Earnings = 20 * Rs. 200 = Rs. 4000
- If he wins at Table C: Earnings = 30 * Rs. 200 = Rs. 6000

3. **Calculating Losses**:
- If he loses at a table, he loses the amount he bet, which is Rs. 200.

4. **Finding Maximum Earnings**:
- The maximum earnings occur when he wins at the two highest payout tables (B and C) and loses at A.
- Earnings from B = Rs. 4000
- Earnings from C = Rs. 6000
- Loss from A = Rs. 200
- Total Maximum Earnings = Rs. 4000 + Rs. 6000 - Rs. 200 = Rs. 9800

5. **Finding Minimum Earnings**:
- The minimum earnings occur when he wins at the lowest payout table (A) and loses at the highest payout tables (B and C).
- Earnings from A = Rs. 2000
- Loss from B = Rs. 200
- Loss from C = Rs. 200
- Total Minimum Earnings = Rs. 2000 - Rs. 200 - Rs. 200 = Rs. 1600

6. **Calculating the Difference**:
- The difference between maximum and minimum earnings = Rs. 9800 - Rs. 1600 = Rs. 8200.

### Final Answer:
The maximum difference between his earnings can be Rs. 8200.