The mean shortly salary of 40 workers of a factory is x in a particular year. Each one was given Rs 30000 as Diwali Bonus. What will be the mean monthly salary in that month.

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the given information
We know that the mean monthly salary of 40 workers is \( x \). This means that the total salary of all workers can be calculated as:
\[ \text{Total Salary} = \text{Mean} \times \text{Number of Workers} = x \times 40 \]

### Step 2: Calculate the total salary before the bonus
The total salary of the 40 workers before receiving the Diwali bonus is:
\[ \text{Total Salary} = 40x \]

### Step 3: Calculate the total bonus given
Each worker received a Diwali bonus of Rs. 30,000. Therefore, the total bonus for all 40 workers is:
\[ \text{Total Bonus} = 30,000 \times 40 = 1,200,000 \]

### Step 4: Calculate the new total salary after the bonus
Now, we will add the total bonus to the original total salary to find the new total salary:
\[ \text{New Total Salary} = \text{Total Salary} + \text{Total Bonus} = 40x + 1,200,000 \]

### Step 5: Calculate the new mean monthly salary
To find the new mean monthly salary, we divide the new total salary by the number of workers:
\[ \text{New Mean} = \frac{\text{New Total Salary}}{\text{Number of Workers}} = \frac{40x + 1,200,000}{40} \]

### Step 6: Simplify the expression for the new mean
We can simplify the expression:
\[ \text{New Mean} = \frac{40x}{40} + \frac{1,200,000}{40} = x + 30,000 \]

### Final Answer
Thus, the new mean monthly salary after adding the Diwali bonus is:
\[ \text{New Mean} = x + 30,000 \]

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