Tata, Hutch and Idea started of with a same. The rule is that the loser of the game distributes `1/3` rd of his money amongst the other two players in the ratio of the amount as they are holding with them. After playing three round game Tata, Hutch and Idea endup with Rs. 450, 150 and 300 respectively. The total amount of money what they were initially holding is:

Options

A. 575
B. 750
C. `5/4 (6!)`
D. can't be determined

Answer

To solve the problem step by step, we need to analyze the situation where Tata, Hutch, and Idea started with the same amount of money and ended up with different amounts after three rounds of a game.

### Step 1: Define the initial amount
Let the initial amount of money that each player started with be \( x \). Therefore, initially:
- Tata = \( x \)
- Hutch = \( x \)
- Idea = \( x \)

### Step 2: Understand the distribution rule
According to the rule, the loser of each round gives away \( \frac{1}{3} \) of their money to the other two players in the ratio of the amounts they currently hold.

### Step 3: Analyze the final amounts
After three rounds, the final amounts are:
- Tata = Rs. 450
- Hutch = Rs. 150
- Idea = Rs. 300

### Step 4: Calculate the total final amount
The total amount of money after three rounds is:
\[ 450 + 150 + 300 = 900 \]

### Step 5: Determine the initial total amount
Since the total amount of money remains constant throughout the game, the initial total amount must also be Rs. 900. Thus:
\[ 3x = 900 \]

### Step 6: Solve for \( x \)
To find the initial amount \( x \), divide the total by 3:
\[ x = \frac{900}{3} = 300 \]

### Conclusion
Therefore, each player initially had Rs. 300.

### Final Answer
The total amount of money that they were initially holding is Rs. 900.

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