Rs 700 is divided among . A ,B and C so that A receives half as much as B and B half as much as C . Then C's share is

Options

A. Rs 200
B. Rs 300
C. Rs 400
D. Rs 600

Answer

To solve the problem, we need to divide Rs 700 among A, B, and C based on the given conditions. Let's break it down step by step.

### Step 1: Define the relationships
According to the problem:
- A receives half as much as B: \( A = \frac{1}{2}B \)
- B receives half as much as C: \( B = \frac{1}{2}C \)

### Step 2: Express A and B in terms of C
From the second relationship, we can express B in terms of C:
\[ B = \frac{1}{2}C \]

Now, substituting this into the first relationship:
\[ A = \frac{1}{2}B = \frac{1}{2} \left(\frac{1}{2}C\right) = \frac{1}{4}C \]

### Step 3: Write the total sum equation
Now we can express the total amount distributed among A, B, and C:
\[ A + B + C = 700 \]

Substituting the expressions for A and B in terms of C:
\[ \frac{1}{4}C + \frac{1}{2}C + C = 700 \]

### Step 4: Combine the terms
To combine the terms, we need a common denominator. The common denominator for 4 and 2 is 4:
\[ \frac{1}{4}C + \frac{2}{4}C + \frac{4}{4}C = 700 \]
\[ \frac{1 + 2 + 4}{4}C = 700 \]
\[ \frac{7}{4}C = 700 \]

### Step 5: Solve for C
Now, we can solve for C:
\[ C = 700 \times \frac{4}{7} \]
\[ C = 400 \]

### Conclusion
C's share is Rs 400.