John owns a cleaning company that cleans office blocks. The number of employees in his company and their salaries in 2020 are as follows. 11 handymen, each receiving a yearly salary of $45 936. 272 cleaners, each receiving$5.20 per hour and working 8 hours per day for a total of 20 days per month.
12 supervisors, men and women in the ratio 1 : 3, each receiving a monthly salary that is 235% more than a cleaner’s monthly salary.
11 drivers, each receiving $594.50 per week, for 4 weeks in a month. In addition, both employer and employee must contribute a portion of the employee’s monthly salary to the Central Provident Fund (CPF).
The table shows the CPF contribution and allocation rates for Singapore citizens.

1. Express the 2020 salary as a percentage of the 2017 salary.

Since the 2020 salary is $2.5\%$ more than the 2017 salary,

$\text{2020 salary} = 100\% + 2.5\% = 102.5\% \text{ of 2017 salary}.$

2. Find the 2017 salary by dividing by the percentage multiplier.

Let the 2017 salary be $x$.

$102.5\% \times x = 45\,936$

$1.025x = 45\,936$

$x = \frac{45\,936}{1.025} = 44\,816$

1. Find Mdm Lee's monthly salary as a cleaner.

Cleaner monthly salary
$= \$5.20 \times 8 \times 20 = \$832$

2. Use the CPF rates for age 65 and calculate the total CPF contribution.

For age 65, use the rates for above 60 to 65:

Employer contribution $= 9\%$, employee contribution $= 7.5\%$.

Total contribution rate
$= 9\% + 7.5\% = 16.5\%$

Total monthly CPF contribution
$= 16.5\% \times 832$
$= 0.165 \times 832 = \$137.28$

1. Find the number of male supervisors and the total number of employees.

Supervisors are men and women in the ratio $1:3$.

Total parts $=1+3=4$.

Number of male supervisors
$=\frac{1}{4}\times 12=3.$

Total number of employees
$=11+272+12+11=306.$

2. Calculate the probability and justify the comment.

Probability of selecting a male supervisor
$=\frac{3}{306}=\frac{1}{102}\approx 0.0098=0.98\%.$

This probability is very small, so the event is most unlikely.

1. Find the monthly salary for each type of employee.

Cleaner’s monthly salary:
$5.20 \times 8 \times 20 = \char36{}832$

Handyman’s monthly salary:
$\dfrac{45936}{12}=\char36{}3828$

Supervisor’s monthly salary:
$832 \times 335\% = 832 \times 3.35 = \char36{}2787.20$

Driver’s monthly salary:
$594.50 \times 4 = \char36{}2378$

2. Find the total monthly salary paid to all employees.

Total monthly salary
$=11(3828)+272(832)+12(2787.20)+11(2378)$
$=42108+226304+33446.40+26158$
$=\$328016.40$

3. Find the mean monthly salary of all employees.

Total number of employees:
$11+272+12+11=306$

Mean monthly salary:
$\dfrac{328016.40}{306}=\$1071.95\text{ approximately}$

4. Express the difference between the lowest salary and the mean salary as a percentage of the mean salary, then verify the statement.

The lowest paid employees are the cleaners, with monthly salary $\char36{}832$.

Difference:
$1071.95-832=\$239.95$

Percentage of the mean salary:
$\dfrac{239.95}{1071.95}\times 100\%=22.4\%\text{ approximately}$

Since $22.4\%<25\%$, John’s statement is valid.