Rs 1521/- is divided among three persons A, B and C. What is B's share ?
(I) B gets Rs 54 more than the average share.
(III) A and C gets Rs 399 more than what B gets.

Options

A. 555
B. 507
C. 561
D. 554

Answer

To find B's share from the total amount of Rs 1521 divided among A, B, and C, we can follow these steps:

### Step 1: Calculate the Average Share
The total amount is Rs 1521, and it is divided among three persons (A, B, and C).

\[ \text{Average Share} = \frac{\text{Total Amount}}{\text{Number of Persons}} = \frac{1521}{3} = 507 \]

### Step 2: Determine B's Share
According to the problem, B gets Rs 54 more than the average share.

\[ B's \text{ Share} = \text{Average Share} + 54 = 507 + 54 = 561 \]

### Step 3: Verify with the Conditions
We also have a second condition stating that A and C together get Rs 399 more than what B gets.

Let A's share be \( A \) and C's share be \( C \). According to the condition:

\[ A + C = B + 399 \]

Substituting B's share:

\[ A + C = 561 + 399 = 960 \]

### Step 4: Check Total Shares
Now, we can check if the total of A, B, and C equals Rs 1521:

\[ A + B + C = 1521 \]

Substituting B's share and the sum of A and C:

\[ 960 + 561 = 1521 \]

This confirms that our calculations are correct.

### Final Answer
Thus, B's share is Rs 561.

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