In a factory ratio of number of 3 categories (A, B and C) of workers is 10 : 7:4. If number of workers in category C is 54 and income of total worker in category B is Rs 1400. Find the total income of workers of category A.

Options

A. Rs 2000
B. Rs 2400
C. Rs 3600
D. Rs 4800

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the ratio of workers
The ratio of workers in categories A, B, and C is given as:
- A : B : C = 10 : 7 : 4

### Step 2: Find the total parts in the ratio
To find the total number of parts in the ratio, we add the parts together:
- Total parts = 10 + 7 + 4 = 21 parts

### Step 3: Determine the number of workers in each category
We know that the number of workers in category C is 54. Since C corresponds to 4 parts in the ratio, we can set up a proportion to find the number of workers in each category.

Let the number of workers in category C be represented as:
- Workers in C = (4 parts / 21 parts) * Total Workers

Setting this equal to 54:
\[ \frac{4}{21} \times \text{Total Workers} = 54 \]

To find the total number of workers, we can rearrange this equation:
\[ \text{Total Workers} = 54 \times \frac{21}{4} \]
\[ \text{Total Workers} = 54 \times 5.25 = 283.5 \]

Since the number of workers must be a whole number, we can find the number of workers in each category directly from the ratio.

### Step 4: Calculate the number of workers in each category
Using the ratio, we can find the number of workers in each category:
- Workers in A = (10/21) * Total Workers
- Workers in B = (7/21) * Total Workers
- Workers in C = (4/21) * Total Workers = 54

From the ratio, we can find:
- Workers in A = (10/4) * 54 = 135
- Workers in B = (7/4) * 54 = 94.5 (not possible, so we need to recalculate based on the total workers)

### Step 5: Calculate the income of workers in category B
We know the total income of workers in category B is Rs 1400. To find the income per worker in B:
- Income per worker in B = Total Income of B / Number of workers in B

### Step 6: Find the income of workers in category A
To find the total income of workers in category A, we first need to find the number of workers in A and then multiply it by the income per worker (which we can assume is the same for all categories unless stated otherwise).

### Final Calculation
Assuming the income per worker is the same across categories, we can calculate the total income for category A.

Let’s summarize:
- Workers in A = 135
- Workers in B = 94.5 (we will round this to the nearest whole number)
- Workers in C = 54

Now, we can calculate the total income for A based on the income per worker derived from B.

### Conclusion
The total income of workers in category A can be calculated as follows:
- Total Income of A = (Number of workers in A) * (Income per worker)

Assuming the income per worker is consistent, we can derive the total income for A.