A certain sum of money was divided between A,B and C in the ratio `5:6:9` . If A received Rs. 450 , the sum divided was

Options

A. Rs. 2000
B. Rs. 1800
C. Rs. 2250
D. Rs.1000

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the ratio
The money is divided between A, B, and C in the ratio of 5:6:9. This means that for every 5 parts A receives, B receives 6 parts, and C receives 9 parts.

### Step 2: Calculate the total parts in the ratio
Add the parts of the ratio together:
- A's part = 5
- B's part = 6
- C's part = 9

Total parts = 5 + 6 + 9 = 20

### Step 3: Determine A's share in terms of total amount
Let the total sum of money be represented by \( x \). Since A's share corresponds to 5 parts out of the total 20 parts, we can express A's share as:
\[ \text{A's share} = \frac{5}{20} \times x = \frac{x}{4} \]

### Step 4: Set up the equation with the known value
We know from the problem that A received Rs. 450. Therefore, we can set up the equation:
\[ \frac{x}{4} = 450 \]

### Step 5: Solve for \( x \)
To find \( x \), multiply both sides of the equation by 4:
\[ x = 450 \times 4 \]
\[ x = 1800 \]

### Step 6: Conclusion
The total sum of money that was divided among A, B, and C is Rs. 1800.