Rs 4900 are divided among three workers in the ratio `3/4 :2:4/3` .The share (in Rs) of the second worker is

Answer

To find the share of the second worker when Rs 4900 is divided among three workers in the ratio \( \frac{3}{4} : 2 : \frac{4}{3} \), we can follow these steps:

### Step 1: Convert the Ratios to a Common Denominator
The given ratios are \( \frac{3}{4}, 2, \frac{4}{3} \). To work with these ratios, we need to express them with a common denominator. The denominators are 4 and 3. The least common multiple (LCM) of 4 and 3 is 12.

- Convert \( \frac{3}{4} \) to have a denominator of 12:
\[ \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \]

- Convert \( 2 \) to have a denominator of 12:
\[ 2 = \frac{2 \times 12}{1 \times 12} = \frac{24}{12} \]

- Convert \( \frac{4}{3} \) to have a denominator of 12:
\[ \frac{4}{3} = \frac{4 \times 4}{3 \times 4} = \frac{16}{12} \]

Now, the ratios can be expressed as:
\[ 9 : 24 : 16 \]

### Step 2: Assign Variables to Each Share
Let the shares of the three workers be represented as:
- First worker: \( 9x \)
- Second worker: \( 24x \)
- Third worker: \( 16x \)

### Step 3: Set Up the Equation
According to the problem, the total amount distributed among the workers is Rs 4900. Therefore, we can set up the equation:
\[ 9x + 24x + 16x = 4900 \]

### Step 4: Simplify the Equation
Combine the terms on the left side:
\[ 49x = 4900 \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides by 49:
\[ x = \frac{4900}{49} = 100 \]

### Step 6: Calculate the Share of the Second Worker
Now that we have the value of \( x \), we can find the share of the second worker:
\[ \text{Share of second worker} = 24x = 24 \times 100 = 2400 \]

### Final Answer
The share of the second worker is Rs 2400.

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