Rs. 395 are divided among A,B and C, in such a manner that B gets 25 per cent more than A and 20 per cent more than C. The share of A will be

Options

A. Rs. 195
B. Rs. 180
C. Rs. 98
D. Rs. 120

Answer

To solve the problem of dividing Rs. 395 among A, B, and C, we will follow these steps:

### Step 1: Define the shares
Let A's share be denoted as \( x \).

### Step 2: Calculate B's share
Since B gets 25% more than A, we can express B's share as:
\[ B = A + 0.25A = 1.25A = 1.25x \]

### Step 3: Calculate C's share
B also gets 20% more than C. To find C's share, we can set up the equation:
\[ B = C + 0.20C = 1.20C \]
From this, we can express C in terms of B:
\[ C = \frac{B}{1.20} = \frac{1.25x}{1.20} \]
Calculating this gives:
\[ C = \frac{1.25}{1.20}x = \frac{25}{24}x \]

### Step 4: Set up the equation for total shares
Now, we can express the total amount distributed among A, B, and C:
\[ A + B + C = x + 1.25x + \frac{25}{24}x = 395 \]

### Step 5: Combine the shares
To combine the shares, we need a common denominator. The common denominator for \( 1 \), \( 1.25 \), and \( \frac{25}{24} \) is \( 24 \):
\[ x = \frac{24}{24}x, \quad 1.25x = \frac{30}{24}x, \quad C = \frac{25}{24}x \]
Now adding these together:
\[ \frac{24}{24}x + \frac{30}{24}x + \frac{25}{24}x = 395 \]
This simplifies to:
\[ \frac{79}{24}x = 395 \]

### Step 6: Solve for x
To find \( x \), we multiply both sides by \( \frac{24}{79} \):
\[ x = 395 \times \frac{24}{79} \]
Calculating this gives:
\[ x = \frac{9480}{79} = 120 \]

### Step 7: Conclusion
Thus, A's share is:
\[ \text{A's share} = x = 120 \]

### Final Answer
The share of A will be Rs. 120.

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