In a office the number of officer decrease in the ratio 11:9. There daily wages increase in the ratio 12 : 19. Then the total wages increase of one day is Rs. 19500. Then what was the starting wages.

Options

A. 66000
B. 60000
C. 55000
D. 44000

Answer

To solve the problem step by step, we will first define the variables and then calculate the starting wages based on the given ratios and the increase in total wages.

### Step 1: Define the Variables
Let:
- The initial number of officers be represented as \( 11x \) (where \( x \) is a common multiplier).
- The new number of officers after the decrease be represented as \( 9x \).
- The initial daily wage per officer be represented as \( 12y \) (where \( y \) is another common multiplier).
- The new daily wage per officer after the increase be represented as \( 19y \).

### Step 2: Calculate the Initial and New Total Wages
- The initial total wages for all officers:
\[ \text{Initial Total Wages} = \text{Number of Officers} \times \text{Daily Wage} = 11x \times 12y = 132xy \]

- The new total wages for all officers after the decrease and increase:
\[ \text{New Total Wages} = \text{New Number of Officers} \times \text{New Daily Wage} = 9x \times 19y = 171xy \]

### Step 3: Calculate the Increase in Total Wages
The increase in total wages is given as:
\[ \text{Increase in Total Wages} = \text{New Total Wages} - \text{Initial Total Wages} \]
Substituting the values we calculated:
\[ 171xy - 132xy = 39xy \]
According to the problem, this increase is equal to Rs. 19,500:
\[ 39xy = 19500 \]

### Step 4: Solve for \( xy \)
To find \( xy \):
\[ xy = \frac{19500}{39} = 500 \]

### Step 5: Calculate the Initial Wages
Now, we need to find the starting wages which is \( 132xy \):
\[ \text{Starting Wages} = 132xy = 132 \times 500 = 66000 \]

### Final Answer
The starting wages were Rs. 66,000.

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