There are 50 boxes and 50 persons. Person 1 keeps 1 marble in every box. Person 2 keeps 2 marbles in every 2nd box, person 3 keeps 3 marbles in every third box. This process goes on till person 50 keeps 50 marbles in the 50th box. Find the total number of marbles kept in the 50th box.

Options

A. 43
B. 78
C. 6
D. 93

Answer

To solve the problem of how many marbles are kept in the 50th box, we need to consider the contributions from each person based on the rules provided.

### Step-by-Step Solution:

1. **Understanding the Contributions**:
Each person contributes marbles to the boxes based on their number. Person 1 puts 1 marble in every box, Person 2 puts 2 marbles in every 2nd box, Person 3 puts 3 marbles in every 3rd box, and so on, up to Person 50 who puts 50 marbles in the 50th box.

2. **Identifying the Relevant Persons for Box 50**:
We need to determine which persons contribute to the 50th box. A person contributes to the 50th box if their number is a divisor of 50.

3. **Finding the Divisors of 50**:
The divisors of 50 are:
- 1 (Person 1)
- 2 (Person 2)
- 5 (Person 5)
- 10 (Person 10)
- 25 (Person 25)
- 50 (Person 50)

4. **Calculating the Total Contribution**:
Now we calculate how many marbles each of these persons contributes to the 50th box:
- Person 1 contributes 1 marble.
- Person 2 contributes 2 marbles.
- Person 5 contributes 5 marbles.
- Person 10 contributes 10 marbles.
- Person 25 contributes 25 marbles.
- Person 50 contributes 50 marbles.

5. **Adding Up the Contributions**:
Now, we sum these contributions:
\[ 1 + 2 + 5 + 10 + 25 + 50 = 93 \]

6. **Conclusion**:
Therefore, the total number of marbles kept in the 50th box is **93**.