If Rs.510 be divided among A, B and C in such a way that A gets `(2)/(3)` of what B gets and B gets `(1)/(4)` of what C gets, then their shares are respectively.

Options

A. Rs 150, Rs 240, Rs 120
B. Rs 60, Rs 90, Rs 360
C. Rs 120, Rs 240, Rs 150
D. Rs 150, Rs 300, Rs 60

Answer

To solve the problem of dividing Rs. 510 among A, B, and C based on the given conditions, we can follow these steps:

### Step 1: Define Variables
Let the share of C be denoted as \( x \).

### Step 2: Express Shares of A and B in Terms of C
According to the problem:
- B gets \( \frac{1}{4} \) of what C gets. Therefore, B's share can be expressed as:
\[ B = \frac{x}{4} \]
- A gets \( \frac{2}{3} \) of what B gets. Therefore, A's share can be expressed as:
\[ A = \frac{2}{3} \times B = \frac{2}{3} \times \frac{x}{4} = \frac{2x}{12} = \frac{x}{6} \]

### Step 3: Calculate Total Shares
Now, we can express the total shares of A, B, and C:
\[ \text{Total} = A + B + C = \frac{x}{6} + \frac{x}{4} + x \]

### Step 4: Find a Common Denominator
To add these fractions, we need a common denominator. The least common multiple of 6, 4, and 1 is 12. Thus, we convert each term:
- \( A = \frac{x}{6} = \frac{2x}{12} \)
- \( B = \frac{x}{4} = \frac{3x}{12} \)
- \( C = x = \frac{12x}{12} \)

Now, we can add them:
\[ \text{Total} = \frac{2x}{12} + \frac{3x}{12} + \frac{12x}{12} = \frac{17x}{12} \]

### Step 5: Set Up the Equation
According to the problem, the total amount is Rs. 510:
\[ \frac{17x}{12} = 510 \]

### Step 6: Solve for x
To find \( x \), we multiply both sides by 12:
\[ 17x = 510 \times 12 \]
\[ 17x = 6120 \]
Now, divide both sides by 17:
\[ x = \frac{6120}{17} = 360 \]

### Step 7: Calculate Shares of A and B
Now that we have \( x = 360 \), we can find the shares of A and B:
- C's share:
\[ C = x = 360 \]
- B's share:
\[ B = \frac{x}{4} = \frac{360}{4} = 90 \]
- A's share:
\[ A = \frac{x}{6} = \frac{360}{6} = 60 \]

### Final Shares
Thus, the shares of A, B, and C are:
- A = Rs. 60
- B = Rs. 90
- C = Rs. 360

### Conclusion
The final answer is:
- A's share: Rs. 60
- B's share: Rs. 90
- C's share: Rs. 360