Divide Rs. 3444 among A, B and C such that A gets `3/4` th of B's share and C gets `2/5` th of A's share. What is the share (in Rs) of B?

Options

A. 1680
B. 2200
C. 1800
D. 2500

Answer

To solve the problem of dividing Rs. 3444 among A, B, and C based on the given conditions, we can follow these steps:

### Step 1: Define the Shares
Let the share of B be represented as \( B \). According to the problem:
- A gets \( \frac{3}{4} \) of B's share, which can be expressed as:
\[ A = \frac{3}{4}B \]
- C gets \( \frac{2}{5} \) of A's share, which can be expressed as:
\[ C = \frac{2}{5}A = \frac{2}{5} \left(\frac{3}{4}B\right) = \frac{3}{10}B \]

### Step 2: Express All Shares in Terms of B
Now we have:
- \( A = \frac{3}{4}B \)
- \( B = B \)
- \( C = \frac{3}{10}B \)

### Step 3: Find the Total Parts
To find the total parts, we need to express A, B, and C in a common denominator:
- The denominators are 4, 1, and 10. The least common multiple (LCM) of these numbers is 20.

Now we convert each share:
- For A:
\[ A = \frac{3}{4}B = \frac{3 \times 5}{4 \times 5}B = \frac{15}{20}B \]
- For B:
\[ B = \frac{20}{20}B \]
- For C:
\[ C = \frac{3}{10}B = \frac{3 \times 2}{10 \times 2}B = \frac{6}{20}B \]

### Step 4: Calculate the Total Parts
Now we can sum up the parts:
\[ A + B + C = \frac{15}{20}B + \frac{20}{20}B + \frac{6}{20}B = \frac{15 + 20 + 6}{20}B = \frac{41}{20}B \]

### Step 5: Set Up the Equation
The total amount of money is Rs. 3444. Therefore, we can set up the equation:
\[ \frac{41}{20}B = 3444 \]

### Step 6: Solve for B
To find B, we multiply both sides by \( \frac{20}{41} \):
\[ B = 3444 \times \frac{20}{41} \]

### Step 7: Calculate B
Calculating \( B \):
\[ B = \frac{3444 \times 20}{41} = \frac{68880}{41} = 1680 \]

### Conclusion
The share of B is Rs. 1680.

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