A sum of Rs.2200 has been divided among A,B and C such that A gets `(1/4)` of what B gets and B gets `(1/5)` of what C gets. What is B's share ?

Options

A. 341
B. 364
C. 372
D. 352

Answer

To find B's share from the total sum of Rs. 2200 divided among A, B, and C, we can follow these steps:

### Step 1: Define Variables
Let the amount B receives be denoted as \( B \). According to the problem:
- A gets \( \frac{1}{4} \) of what B gets:
\[ A = \frac{1}{4}B \]
- B gets \( \frac{1}{5} \) of what C gets:
\[ B = \frac{1}{5}C \implies C = 5B \]

### Step 2: Express A, B, and C in terms of B
Now we can express A and C in terms of B:
- From \( A = \frac{1}{4}B \)
- From \( C = 5B \)

### Step 3: Write the Total Sum Equation
The total amount distributed among A, B, and C is Rs. 2200:
\[ A + B + C = 2200 \]
Substituting the expressions for A and C:
\[ \frac{1}{4}B + B + 5B = 2200 \]

### Step 4: Combine Like Terms
Combine the terms on the left side:
\[ \frac{1}{4}B + 1B + 5B = \frac{1}{4}B + \frac{4}{4}B + \frac{20}{4}B = \frac{25}{4}B \]
So, we have:
\[ \frac{25}{4}B = 2200 \]

### Step 5: Solve for B
To isolate B, multiply both sides by \( \frac{4}{25} \):
\[ B = 2200 \times \frac{4}{25} \]
Calculating this:
\[ B = 2200 \times \frac{4}{25} = 2200 \div 25 \times 4 = 88 \times 4 = 352 \]

### Conclusion
Thus, B's share is Rs. 352.

---