Rs 6,400 are divided among three workers In the ratio. `3/5: 2: 5/3`. The share (in rupees) of the second worker is:

Options

A. 3200
B. 3840
C. 2560
D. 3000

Answer

To solve the problem of dividing Rs 6,400 among three workers in the ratio \( \frac{3}{5} : 2 : \frac{5}{3} \), we will follow these steps:

### Step 1: Express the Ratios in a Common Format
First, we need to express the ratios in a common format. The given ratios are \( \frac{3}{5} \), \( 2 \), and \( \frac{5}{3} \). To do this, we will convert all the ratios to have a common denominator.

### Step 2: Find the Least Common Multiple (LCM)
The denominators in the ratios are 5 and 3. The LCM of 5 and 3 is 15. We will now convert each ratio to have 15 as the denominator.

- For \( \frac{3}{5} \):
\[ \frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15} \]

- For \( 2 \):
\[ 2 = \frac{2 \times 15}{1 \times 15} = \frac{30}{15} \]

- For \( \frac{5}{3} \):
\[ \frac{5}{3} = \frac{5 \times 5}{3 \times 5} = \frac{25}{15} \]

### Step 3: Write the Ratios
Now we can write the ratios of the workers A, B, and C as:
\[ A : B : C = 9 : 30 : 25 \]

### Step 4: Calculate the Total Parts
Next, we calculate the total number of parts in the ratio:
\[ Total = 9 + 30 + 25 = 64 \]

### Step 5: Find the Value of One Part
Now, we need to find the value of one part. We do this by dividing the total amount (Rs 6,400) by the total number of parts (64):
\[ Value\ of\ one\ part = \frac{6400}{64} = 100 \]

### Step 6: Calculate the Share of the Second Worker
The second worker (B) has 30 parts. Therefore, the share of the second worker is:
\[ Share\ of\ B = 30 \times 100 = 3000 \]

### Final Answer
The share of the second worker is Rs 3,000.

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