Vadant disributes 385 marbles between Purab and Arya such that Purab gets `4.5 times the marbles that Arya gets. How much does each boy gets ?

Answer

To solve the problem of distributing 385 marbles between Purab and Arya, where Purab receives 4.5 times the number of marbles that Arya receives, we can follow these steps:

### Step-by-Step Solution:

1. **Define Variables**:
Let the number of marbles Arya receives be \( y \). Then the number of marbles Purab receives can be expressed as \( 4.5y \).

2. **Set Up the Equation**:
According to the problem, the total number of marbles distributed is 385. Therefore, we can write the equation:
\[ y + 4.5y = 385 \]

3. **Combine Like Terms**:
Combine the terms on the left side of the equation:
\[ 5.5y = 385 \]

4. **Solve for \( y \)**:
To find \( y \), divide both sides of the equation by 5.5:
\[ y = \frac{385}{5.5} \]
To simplify, we can multiply both numerator and denominator by 10 to eliminate the decimal:
\[ y = \frac{3850}{55} \]
Now, divide 3850 by 55:
\[ y = 70 \]

5. **Calculate Purab's Marbles**:
Now that we have Arya's marbles, we can find out how many marbles Purab receives:
\[ \text{Purab's marbles} = 4.5y = 4.5 \times 70 = 315 \]

6. **Final Answer**:
Therefore, Arya receives 70 marbles and Purab receives 315 marbles.

### Summary:
- Arya gets: **70 marbles**
- Purab gets: **315 marbles**