The table shows the monthly contributions and expenditure pattern of an employee in 1999. Item Percentage Pension 5 Income Tax 25 Food 40 Transport 10 Rent ...

Answer Details

The percentages account for the whole salary, and they sum to

\[5+25+40+10+12.5+7.5 = 100.\]

(a) Pie chart

The whole circle is \(360^\circ\), representing \(100\%\). Each item's sector angle is its percentage multiplied by \(\dfrac{360^\circ}{100} = 3.6^\circ\) per unit:

Item	Percentage (%)	Sector angle
Pension	5	\(\frac{5}{100}\times360^\circ = 18^\circ\)
Income Tax	25	\(\frac{25}{100}\times360^\circ = 90^\circ\)
Food	40	\(\frac{40}{100}\times360^\circ = 144^\circ\)
Transport	10	\(\frac{10}{100}\times360^\circ = 36^\circ\)
Rent	12.5	\(\frac{12.5}{100}\times360^\circ = 45^\circ\)
Others	7.5	\(\frac{7.5}{100}\times360^\circ = 27^\circ\)
Total	100	\(360^\circ\)

Check: \(18^\circ+90^\circ+144^\circ+36^\circ+45^\circ+27^\circ = 360^\circ.\) The completed pie chart is:

(b) Salary calculations (gross monthly salary \(=\) N10,800.00)

(i) Pension contribution \(= 5\%\) of N10,800, i.e. the \(18^\circ\) sector:

\[\frac{5}{100}\times 10800 \;=\; \frac{18}{360}\times 10800 \;=\; \text{N}540.00.\]

(ii) Income tax \(= 25\%\) of N10,800, i.e. the \(90^\circ\) sector:

\[\frac{25}{100}\times 10800 \;=\; \frac{90}{360}\times 10800 \;=\; \text{N}2{,}700.00.\]

(c) Take-home pay

Deduct the pension and income tax from the gross salary. Together they are \((5+25)\% = 30\%\), so the take-home pay is \(100\% - 30\% = 70\%\):

\[10800 - 540 - 2700 \;=\; \frac{70}{100}\times 10800 \;=\; \text{N}7{,}560.00.\]

The employee's take-home pay is N7,560.00.