Divide Rs. 2,600 among A, B, C in the ratio `1/2 : 1/3 : 1/4` . Find the share of each.

Options

A. Rs. 1,200 , Rs. 600, Rs. 800
B. Rs. 1,200 , Rs. 800, Rs. 600
C. Rs. 600, Rs. 800 , Rs. 1,200
D. Rs. 800 , Rs. 600 , Rs. 1,200

Answer

To solve the problem of dividing Rs. 2,600 among A, B, and C in the ratio of \( \frac{1}{2} : \frac{1}{3} : \frac{1}{4} \), we can follow these steps:

### Step 1: Convert the ratios to a common format
The given ratios are \( \frac{1}{2} \), \( \frac{1}{3} \), and \( \frac{1}{4} \). To compare them easily, we can find a common denominator. The least common multiple (LCM) of the denominators (2, 3, and 4) is 12.

### Step 2: Express each ratio with the common denominator
Now we convert each fraction to have the denominator of 12:
- For \( \frac{1}{2} \): \( \frac{1}{2} = \frac{6}{12} \)
- For \( \frac{1}{3} \): \( \frac{1}{3} = \frac{4}{12} \)
- For \( \frac{1}{4} \): \( \frac{1}{4} = \frac{3}{12} \)

Thus, the ratios become:
- A : B : C = 6 : 4 : 3

### Step 3: Calculate the total parts of the ratio
Now, we add the parts of the ratio together:
- Total parts = \( 6 + 4 + 3 = 13 \)

### Step 4: Find the value of each part
To find the value of one part, we divide the total amount (Rs. 2,600) by the total parts (13):
- Value of one part \( x = \frac{2600}{13} = 200 \)

### Step 5: Calculate the share of each person
Now we can find the share of A, B, and C by multiplying the number of parts each person receives by the value of one part:
- Share of A = \( 6x = 6 \times 200 = 1200 \)
- Share of B = \( 4x = 4 \times 200 = 800 \)
- Share of C = \( 3x = 3 \times 200 = 600 \)

### Final Shares
- A's share: Rs. 1,200
- B's share: Rs. 800
- C's share: Rs. 600

### Summary of the Solution
- A receives Rs. 1,200
- B receives Rs. 800
- C receives Rs. 600