Three friends divide `Rs. 624` among themselves in the ratio `1/2 :1/3:1/4`. The share of the third friend is -

Options

A. Rs. 288
B. Rs. 192
C. Rs. 148
D. Rs. 144

Answer

To solve the problem of dividing Rs. 624 among three friends 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 \( \frac{1}{2}, \frac{1}{3}, \frac{1}{4} \). To compare these ratios easily, we can convert them into a common ratio format by finding the least common multiple (LCM) of the denominators.

**Hint:** Find the LCM of the denominators (2, 3, and 4) to simplify the ratios.

### Step 2: Find the LCM
The LCM of 2, 3, and 4 is 12.

**Hint:** The LCM is the smallest number that all the denominators can divide into without leaving a remainder.

### Step 3: Convert Each Fraction to Have the Same Denominator
Now, we can convert each fraction to have the LCM as the denominator:
- For \( \frac{1}{2} \): \( \frac{1 \times 6}{2 \times 6} = \frac{6}{12} \)
- For \( \frac{1}{3} \): \( \frac{1 \times 4}{3 \times 4} = \frac{4}{12} \)
- For \( \frac{1}{4} \): \( \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \)

Thus, the ratios become \( 6 : 4 : 3 \).

**Hint:** Multiply each fraction by the same number to get equivalent ratios.

### Step 4: Sum the Parts of the Ratio
Now, we add the parts of the ratio:
\[ 6 + 4 + 3 = 13 \]

**Hint:** The total parts of the ratio will help us determine how much each part is worth in terms of the total amount.

### Step 5: Find the Value of One Part
Next, we can find the value of one part by dividing the total amount (Rs. 624) by the total number of parts (13):
\[ \text{Value of one part} = \frac{624}{13} = 48 \]

**Hint:** Divide the total amount by the sum of the ratio parts to find the value of one part.

### Step 6: Calculate the Share of Each Friend
Now we can calculate the share of each friend:
- Friend A's share: \( 6 \times 48 = 288 \)
- Friend B's share: \( 4 \times 48 = 192 \)
- Friend C's share: \( 3 \times 48 = 144 \)

**Hint:** Multiply the value of one part by the number of parts each friend has in the ratio.

### Step 7: Identify the Share of the Third Friend
The share of the third friend (Friend C) is:
\[ 3 \times 48 = 144 \]

Thus, the share of the third friend is **Rs. 144**.

**Final Answer:** The share of the third friend is **Rs. 144**.