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. Rs. 600
B. Rs. 1000
C. Rs. 900
D. Rs. 1200

Answer

To solve the problem of distributing Rs. 9000 among A, B, and C in the ratio 4:5:6 and finding the difference between A's and C's shares, 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 Total Parts in the Ratio
To find the total number of parts, we add the parts of A, B, and C:
\[ \text{Total parts} = 4 + 5 + 6 = 15 \]

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

### Step 4: Calculate A's Share
A's share can be calculated by multiplying the number of parts A receives (which is 4) by the value of one part:
\[ \text{A's share} = 4 \times 600 = 2400 \]

### Step 5: Calculate C's Share
Similarly, C's share can be calculated by multiplying the number of parts C receives (which is 6) by the value of one part:
\[ \text{C's share} = 6 \times 600 = 3600 \]

### Step 6: Calculate the Difference Between A's and C's Shares
Finally, to find the difference between C's share and A's share, we subtract A's share from C's share:
\[ \text{Difference} = \text{C's share} - \text{A's share} = 3600 - 2400 = 1200 \]

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

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