The mean monthly salary of 40 workers of a factory is ₹ x in a particular year. Each one was given ₹ 3000 as Diwali Bonus. What will be the mean monthly salary in that month?
In the above question 20 instead of Bonus , Rs 300 be deducted from each workers salary for April to February , what will be their mean monthly salary for December month?

Answer

To solve the problem step by step, we will break it down into two parts as described in the question.

### Part 1: Calculating the Mean Monthly Salary after Diwali Bonus

1. **Understanding the Initial Mean Salary**:
- The mean monthly salary of 40 workers is given as ₹ x.

2. **Calculating the Total Salary Before Bonus**:
- Total salary of 40 workers = Mean salary × Number of workers = \( x \times 40 \).

3. **Calculating the Total Bonus Given**:
- Each worker receives a Diwali Bonus of ₹ 3000.
- Total bonus for 40 workers = ₹ 3000 × 40 = ₹ 120,000.

4. **Calculating the Total Salary After Bonus**:
- Total salary after bonus = Total salary before bonus + Total bonus
- Total salary after bonus = \( (x \times 40) + 120,000 \).

5. **Calculating the New Mean Monthly Salary**:
- New mean = Total salary after bonus / Number of workers
- New mean = \( \frac{(x \times 40) + 120,000}{40} \).
- Simplifying this gives:
\[ \text{New mean} = x + 3000. \]

### Part 2: Calculating the Mean Monthly Salary after Deduction

1. **Understanding the Deduction**:
- Instead of a bonus, ₹ 300 is deducted from each worker's salary from April to February.

2. **Calculating the Total Deduction**:
- Total deduction for 40 workers = ₹ 300 × 40 = ₹ 12,000.

3. **Calculating the Total Salary After Deduction**:
- Total salary after deduction = Total salary before deduction - Total deduction
- Total salary after deduction = \( (x \times 40) - 12,000 \).

4. **Calculating the New Mean Monthly Salary for December**:
- New mean = Total salary after deduction / Number of workers
- New mean = \( \frac{(x \times 40) - 12,000}{40} \).
- Simplifying this gives:
\[ \text{New mean} = x - 300. \]

### Final Answers:
- The mean monthly salary after the Diwali Bonus is \( x + 3000 \).
- The mean monthly salary for December after the deduction is \( x - 300 \).