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 C is 30 : 1. If a man bets ₹ 200 at each table and win at two of the tables, what is the maximum and minimum difference between his earnings can be?

Options

A. ₹ 2500
B. ₹ 2000
C. ₹ 4000
D. none of these

Answer

To solve the problem, we need to calculate the earnings from each table based on the betting amounts and the respective pay-offs. The man bets ₹200 at each table A, B, and C.

### Step 1: Calculate the earnings from each table if he wins.

1. **Table A (Pay-off 10:1)**:
- Bet: ₹200
- Earnings = Bet × Pay-off = ₹200 × 10 = ₹2000
- Total amount received = Bet + Earnings = ₹200 + ₹2000 = ₹2200

2. **Table B (Pay-off 20:1)**:
- Bet: ₹200
- Earnings = Bet × Pay-off = ₹200 × 20 = ₹4000
- Total amount received = Bet + Earnings = ₹200 + ₹4000 = ₹4200

3. **Table C (Pay-off 30:1)**:
- Bet: ₹200
- Earnings = Bet × Pay-off = ₹200 × 30 = ₹6000
- Total amount received = Bet + Earnings = ₹200 + ₹6000 = ₹6200

### Step 2: Determine the combinations of winning at two tables.

The man can win at two tables out of three. The possible combinations are:
- Win at A and B
- Win at A and C
- Win at B and C

### Step 3: Calculate the total earnings for each combination.

1. **Win at A and B**:
- Total earnings = Earnings from A + Earnings from B
- Total earnings = ₹2200 + ₹4200 = ₹6400

2. **Win at A and C**:
- Total earnings = Earnings from A + Earnings from C
- Total earnings = ₹2200 + ₹6200 = ₹8400

3. **Win at B and C**:
- Total earnings = Earnings from B + Earnings from C
- Total earnings = ₹4200 + ₹6200 = ₹10400

### Step 4: Calculate the maximum and minimum earnings.

- Maximum earnings = ₹10400 (winning at B and C)
- Minimum earnings = ₹6400 (winning at A and B)

### Step 5: Calculate the difference between maximum and minimum earnings.

- Difference = Maximum earnings - Minimum earnings
- Difference = ₹10400 - ₹6400 = ₹4000

### Final Answer:
The maximum difference between his earnings can be ₹4000, and the minimum difference is ₹0 (if he wins at the same two tables).

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