In a factory the number of labour decrease in the ratio 9 : 8 and their salary increase in the ratio 14: 15. If total wages of one day decrease by Rs. 6000. Then find the present salary of each day.

Options

A. 12000
B. 100000
C. 160000
D. 120000

Answer

To solve the problem step by step, we will follow the given ratios and the information provided.

### Step 1: Understand the Ratios
The number of laborers decreases in the ratio of 9:8, and their salaries increase in the ratio of 14:15.

Let:
- The initial number of laborers = 9x
- The new number of laborers = 8x
- The initial salary = 14y
- The new salary = 15y

### Step 2: Calculate Total Wages
The total wages before the decrease can be calculated as:
\[ \text{Total Wages (initial)} = \text{Number of laborers} \times \text{Salary} = (9x) \times (14y) = 126xy \]

The total wages after the decrease can be calculated as:
\[ \text{Total Wages (new)} = \text{Number of laborers} \times \text{Salary} = (8x) \times (15y) = 120xy \]

### Step 3: Set Up the Equation for Decrease in Wages
According to the problem, the total wages decrease by Rs. 6000. Therefore, we can set up the equation:
\[ \text{Total Wages (initial)} - \text{Total Wages (new)} = 6000 \]
\[ 126xy - 120xy = 6000 \]
\[ 6xy = 6000 \]

### Step 4: Solve for xy
Now, we can solve for \( xy \):
\[ xy = \frac{6000}{6} = 1000 \]

### Step 5: Calculate Present Salary
We need to find the present salary, which is represented by the new salary:
\[ \text{New Salary} = 15y \]

To find \( y \), we can express \( y \) in terms of \( xy \):
Since \( xy = 1000 \), we can express \( y \) as:
\[ y = \frac{1000}{x} \]

Now substituting \( y \) in the new salary:
\[ \text{New Salary} = 15y = 15 \left(\frac{1000}{x}\right) = \frac{15000}{x} \]

### Step 6: Calculate Total Present Salary
Now, we need to find the total present salary:
\[ \text{Total Present Salary} = \text{Number of laborers} \times \text{New Salary} = 8x \times \frac{15000}{x} = 120000 \]

Thus, the total present salary is Rs. 120,000.

### Final Answer
The present salary of each day is Rs. 120,000.

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