A sum of Rs. 770 has been divided among A, B amd C in such a way that A receives `2/9 th` of what B and C together receive. Then A's share is

Options

A. Rs. 140
B. Rs. 154
C. Rs. 165
D. Rs. 170

Answer

To find A's share from the total sum of Rs. 770, we can follow these steps:

### Step 1: Understand the relationship between A, B, and C
We know that A receives \( \frac{2}{9} \) of what B and C together receive. Let's denote:
- A's share = \( A \)
- B's share = \( B \)
- C's share = \( C \)

From the problem, we can express this relationship mathematically:
\[ A = \frac{2}{9}(B + C) \]

### Step 2: Express the total amount
The total amount distributed among A, B, and C is Rs. 770. Therefore, we can write:
\[ A + B + C = 770 \]

### Step 3: Substitute B + C in terms of A
From the first equation, we can express \( B + C \) in terms of A:
\[ B + C = \frac{9}{2}A \]

### Step 4: Substitute into the total amount equation
Now, substitute \( B + C \) back into the total amount equation:
\[ A + \frac{9}{2}A = 770 \]

### Step 5: Combine like terms
Combine the terms on the left side:
\[ \frac{11}{2}A = 770 \]

### Step 6: Solve for A
To find A, multiply both sides by \( \frac{2}{11} \):
\[ A = 770 \times \frac{2}{11} \]

### Step 7: Calculate A
Now, calculate the value:
\[ A = \frac{1540}{11} \]
\[ A = 140 \]

Thus, A's share is Rs. 140.

### Final Answer:
A's share is Rs. 140.

---