315 marbles are distributed among Aman, Ashok and Alok in the ratio 7 : 3 : 5, respectively. How many more marbles did Aman get compared to Ashok?

Options

A. 84
B. 42
C. 147
D. 63

Answer

To solve the problem of distributing 315 marbles among Aman, Ashok, and Alok in the ratio of 7:3:5, we can follow these steps:

### Step 1: Calculate the total parts in the ratio
The ratio of marbles distributed among Aman, Ashok, and Alok is 7:3:5. To find the total parts, we add the parts of the ratio together.

\[ \text{Total parts} = 7 + 3 + 5 = 15 \]

### Step 2: Determine the value of one part
Now, we need to find out how much one part is worth. We do this by dividing the total number of marbles by the total parts.

\[ \text{Value of one part} = \frac{\text{Total marbles}}{\text{Total parts}} = \frac{315}{15} = 21 \]

### Step 3: Calculate the number of marbles each person receives
Now we can calculate how many marbles each person gets by multiplying the number of parts they receive by the value of one part.

- **Aman's marbles**:
\[ \text{Aman's marbles} = 7 \times 21 = 147 \]

- **Ashok's marbles**:
\[ \text{Ashok's marbles} = 3 \times 21 = 63 \]

### Step 4: Find out how many more marbles Aman received compared to Ashok
To find out how many more marbles Aman received compared to Ashok, we subtract the number of marbles Ashok received from the number of marbles Aman received.

\[ \text{Difference} = \text{Aman's marbles} - \text{Ashok's marbles} = 147 - 63 = 84 \]

### Final Answer
Aman received 84 more marbles than Ashok.

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