The monthly expenditure of a family on different heads is shown in the following pie chart.

What is the percentage of family earnings spent on rent?

The correct answer is $16\frac{2}{3}$.

From the pie chart titled "Expenditure on different Heads", the following sector angles are clearly labelled:

• Rent = 60°
• Children Education = 70°
• Food = 65°
• Transport = 50°
• Saving = 40°
• Misc Expenses = 75°

Step 1: Verify the total of all angles.

$60+70+65+50+40+75=360°$

✓ The angles correctly add up to 360°, confirming the pie chart data is consistent.

Step 2: Understand the key formula.

In a pie chart, a full circle represents 100% of the total expenditure, and a full circle = 360°. Therefore, the percentage corresponding to any sector is:

$\text{Percentage}=\frac{\text{Sector Angle}}{360}\times 100$

Step 3: Calculate the percentage spent on Rent.

The angle for the Rent sector is 60°. Substituting into the formula:

$\text{Percentage (Rent)}=\frac{60}{360}\times 100$

$=\frac{1}{6}\times 100$

$=\frac{100}{6}$

Step 4: Convert the improper fraction to a mixed number.

Dividing 100 by 6:

$100÷6=16\text{remainder}4$

So:

$\frac{100}{6}=16\frac{4}{6}=16\frac{2}{3}$

Therefore, the percentage of the family's earnings spent on Rent is:

$16\frac{2}{3}\%$