Let's solve the problem step-by-step.
### Part i: Finding the bonus for each employee
The net profit of the cement factory in the last year is Rs 3,60,00,000. The management has decided to distribute 16% of this profit as a bonus to its 120 employees.
1. Calculating the total bonus amount:
The total bonus amount is calculated as 16% of the net profit.
[tex]\[
\text{Total bonus} = \frac{16}{100} \times 3,60,00,000 = 0.16 \times 3,60,00,000 = 57,60,000 \text{ Rs}
\][/tex]
2. Calculating the bonus per employee:
The bonus per employee is found by dividing the total bonus amount by the number of employees.
[tex]\[
\text{Bonus per employee} = \frac{\text{Total bonus}}{120} = \frac{57,60,000}{120} = 48,000 \text{ Rs}
\][/tex]
So, each employee receives a bonus of Rs 48,000.
### Part ii: Determining the percentage increase to reach Rs 60,000 per employee
Next, we need to determine by what percentage the bonus should be increased so that each employee receives Rs 60,000.
1. Calculating the required total bonus:
If each employee is to receive Rs 60,000, the required total bonus amount is:
[tex]\[
\text{Required total bonus} = 60,000 \times 120 = 72,00,000 \text{ Rs}
\][/tex]
2. Calculating the required bonus percentage to meet the target:
To find the new bonus percentage, we use the required total bonus amount and the net profit.
[tex]\[
\text{Required bonus percentage} = \left(\frac{\text{Required total bonus}}{\text{Net profit}}\right) \times 100 = \left(\frac{72,00,000}{3,60,00,000}\right) \times 100 = \frac{72}{360} \times 100 = 20\%
\][/tex]
3. Calculating the percentage increase in the bonus:
Finally, we need to find the increase from the original bonus percentage (16%) to the new bonus percentage (20%).
[tex]\[
\text{Percentage increase} = 20\% - 16\% = 4\%
\][/tex]
Therefore, to have each employee receive Rs 60,000, the bonus needs to be increased by 4%.
