A certain sum of money is distributed among A, B and C in the ratio of ` 1/2 : 1/3 : 1/4` and B gets Rs. 120.
Find the shares of A and C.

Answer

To solve the problem step-by-step, we will follow these steps:

### Step 1: Understand the given ratio
The ratio of the shares of A, B, and C is given as \( \frac{1}{2} : \frac{1}{3} : \frac{1}{4} \).

### Step 2: Find a common denominator
To simplify the ratio, we need to find the least common multiple (LCM) of the denominators 2, 3, and 4.

- The LCM of 2, 3, and 4 is 12.

### Step 3: Convert the ratios to a common form
Now, we will convert each part of the ratio to have the same denominator:

- For A: \( \frac{1}{2} = \frac{6}{12} \)
- For B: \( \frac{1}{3} = \frac{4}{12} \)
- For C: \( \frac{1}{4} = \frac{3}{12} \)

Thus, the simplified ratio is:
\[ A : B : C = 6 : 4 : 3 \]

### Step 4: Set up the equation for B's share
We know that B receives Rs. 120. In the ratio, B's share is represented by 4 parts.

Let the total amount of money be \( x \). Then, B's share can be expressed as:
\[ \frac{4}{(6 + 4 + 3)} \times x = 120 \]

### Step 5: Calculate the total parts
The total parts in the ratio is:
\[ 6 + 4 + 3 = 13 \]

### Step 6: Set up the equation
Now we can express B's share:
\[ \frac{4}{13} \times x = 120 \]

### Step 7: Solve for \( x \)
To find \( x \), we rearrange the equation:
\[ x = 120 \times \frac{13}{4} \]

Calculating this gives:
\[ x = 120 \times 3.25 = 390 \]

### Step 8: Calculate A's share
Now we can find A's share:
\[ A's \, share = \frac{6}{13} \times 390 \]

Calculating this gives:
\[ A's \, share = 6 \times 30 = 180 \]

### Step 9: Calculate C's share
Now we can find C's share:
\[ C's \, share = \frac{3}{13} \times 390 \]

Calculating this gives:
\[ C's \, share = 3 \times 30 = 90 \]

### Final Shares
- A's share = Rs. 180
- C's share = Rs. 90

### Summary of the solution:
- A receives Rs. 180.
- C receives Rs. 90.