A sum of Rs 9000 is to be distributed among A, B and C in the ratio `4:5:6` .What will be the difference between A's and C's shares ?

Options

A. 1300
B. 1500
C. 1400
D. 1200

Answer

To solve the problem of distributing Rs 9000 among A, B, and C in the ratio of 4:5:6, we can follow these steps:

### Step 1: Understand the Ratio
The ratio of A, B, and C is given as 4:5:6. This means that for every 4 parts A receives, B receives 5 parts, and C receives 6 parts.

### Step 2: Calculate the Total Parts
To find the total number of parts in the ratio, we add the parts together:
\[ 4 + 5 + 6 = 15 \]
So, the total parts = 15.

### Step 3: Determine the Value of Each Part
Now, we need to find the value of one part. Since the total amount to be distributed is Rs 9000, we divide this amount by the total number of parts:
\[ \text{Value of one part} = \frac{9000}{15} = 600 \]

### Step 4: Calculate Individual Shares
Now we can calculate the individual shares for A, B, and C:
- A's share = \( 4 \times 600 = 2400 \)
- B's share = \( 5 \times 600 = 3000 \)
- C's share = \( 6 \times 600 = 3600 \)

### Step 5: Find the Difference Between A's and C's Shares
Finally, we need to find the difference between A's share and C's share:
\[ \text{Difference} = C's \, share - A's \, share = 3600 - 2400 = 1200 \]

### Conclusion
The difference between A's and C's shares is Rs 1200.

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