In a factory, the ratio of the numbers of employees of three types A, B and C is 9: 13 :18 and their wages are in the ratio of 10 : 7 : 4. If number of employees of type C is 54 and wages of every employee of type B is 1400, then find the total wages of all the employees of type A.

Options

A. X51000
B. X 54000
C. X 56000
D. X 59000

Answer

To find the total wages of all the employees of type A, we can follow these steps:

### Step 1: Determine the total number of employees for each type based on the given ratio.
The ratio of employees of types A, B, and C is given as 9:13:18. Let the number of employees of type A be \(9k\), type B be \(13k\), and type C be \(18k\).

### Step 2: Use the information about type C to find the value of \(k\).
We know that the number of employees of type C is 54. Therefore, we can set up the equation:
\[ 18k = 54 \]
To find \(k\), we divide both sides by 18:
\[ k = \frac{54}{18} = 3 \]

### Step 3: Calculate the number of employees for each type using \(k\).
Now that we have \(k\), we can find the number of employees for types A and B:
- Employees of type A: \(9k = 9 \times 3 = 27\)
- Employees of type B: \(13k = 13 \times 3 = 39\)
- Employees of type C: \(18k = 18 \times 3 = 54\) (as given)

### Step 4: Determine the wages for each type based on the given wage ratio.
The wages for types A, B, and C are in the ratio 10:7:4. Let the wages of employees of type A be \(10x\), type B be \(7x\), and type C be \(4x\).

### Step 5: Use the information about type B to find the value of \(x\).
We know that the wage of every employee of type B is 1400. Therefore, we set up the equation:
\[ 7x = 1400 \]
To find \(x\), we divide both sides by 7:
\[ x = \frac{1400}{7} = 200 \]

### Step 6: Calculate the wages for type A.
Now we can find the wage for each employee of type A:
\[ \text{Wage of type A} = 10x = 10 \times 200 = 2000 \]

### Step 7: Calculate the total wages for all employees of type A.
The total wages for all employees of type A can be calculated by multiplying the number of employees of type A by the wage of type A:
\[ \text{Total wages of type A} = \text{Number of employees of type A} \times \text{Wage of type A} = 27 \times 2000 = 54000 \]

### Final Answer:
The total wages of all the employees of type A is **54000**.

---