At a casino in Mumbai, there are three tables A, B and C. The payoffs at table A, B and C are 10 : 1, 20 : 1 and 30 : 1 respectively. A man bets Rs 200 at each table and wins at exactly two of the three tables. What is the maximum possible difference between his total earnings in rupees over all such winning combinations?

Introduction / Context:
This question tests understanding of odds and payoffs in a gambling context, combined with basic profit comparison. A man places equal bets on three different tables with different payoff ratios and wins on any two of them. We must analyse the possible total earnings across the different winning combinations and compute the maximum difference between them. It is a nice applied ratio and multiplication problem.

Given Data / Assumptions:

• Three tables A, B and C with payoffs 10 : 1, 20 : 1 and 30 : 1 respectively.
• The man bets Rs 200 on each table, so he bets Rs 600 in total.
• Winning at a table with odds p : 1 gives profit of p times the stake and also returns the stake to the player.
• He wins at exactly two tables and loses at the remaining one.
• We must find the maximum possible difference between his total earnings (net profit) among all such win combinations.

Concept / Approach:
First, compute profit from a single winning bet at each table. Then, for each possible pair of winning tables (A and B, A and C, B and C), sum the profits from the wins and subtract the loss of the stake at the losing table. This gives three possible total profits. The maximum difference in earnings is the difference between the highest and the lowest of these profits. The stake of Rs 200 is common, so the calculation remains straightforward.

Step-by-Step Solution:
Stake at each table = Rs 200. At table A, odds 10 : 1 mean profit = 10 * 200 = Rs 2000. At table B, odds 20 : 1 mean profit = 20 * 200 = Rs 4000. At table C, odds 30 : 1 mean profit = 30 * 200 = Rs 6000. If he wins at A and B and loses at C, total profit = 2000 + 4000 − 200 = Rs 5800. If he wins at A and C and loses at B, total profit = 2000 + 6000 − 200 = Rs 7800. If he wins at B and C and loses at A, total profit = 4000 + 6000 − 200 = Rs 9800. The smallest profit is Rs 5800 and the largest profit is Rs 9800. Maximum difference in earnings = 9800 − 5800 = Rs 4000.

Verification / Alternative check:
We can also focus only on the two winning tables since in each scenario exactly one Rs 200 loss occurs. For winnings from tables A and B, combined profit is 2000 + 4000 = 6000. For A and C, it is 2000 + 6000 = 8000. For B and C, it is 4000 + 6000 = 10000. Subtracting a fixed 200 loss from each gives 5800, 7800 and 9800, which differ pairwise by 2000 and 4000. Hence, the maximum gap between any two outcomes remains Rs 4000.

Why Other Options Are Wrong:
Values like Rs 2500 or Rs 2000 arise if one mixes up higher and lower profits or forgets to consider all three cases. Rs 1500 and Rs 3000 are other arbitrary differences that do not match the computed gap between 5800 and 9800. Only Rs 4000 is consistent with the full analysis of all possibilities.

Common Pitfalls:
Some learners confuse odds expressed as 10 : 1 with a simple multiplier of 11. Here we are interested in profit, so we take the 10 times payment, not adding the stake when computing profit. Others forget to subtract the lost stake at the losing table or consider only one winning combination. Systematically listing all win pairs and computing each outcome prevents such mistakes.

Final Answer:
The maximum possible difference between his earnings across the different winning combinations is Rs 4000.