WAEC 2011 · Paper 2 · Q5

A library received a $1,300 grant. It spends $10\%$ of the grant on magazine subscriptions, $35\%$ on new books, $15\%$ to repair damaged books, $30\%$ to buy new furniture and $10\%$ to train library staff.

(a)
Represent this information on a pie chart.
Separate values with commas, e.g. 3, −2
(b)
Calculate, correct to the nearest whole number, the percentage increase of the amount for buying new books over that of new furniture.

Worked solution (try it first)

(a)

The whole circle, $360^\circ$ , stands for the whole grant, $100\%$ .
So each $1\%$ is $3.6^\circ$ : magazines $10 \times 3.6^\circ = 36^\circ$ , new books $35 \times 3.6^\circ = 126^\circ$ , repairs $54^\circ$ , furniture $108^\circ$ and training $36^\circ$ .
Check: $36 + 126 + 54 + 108 + 36 = 360$ .
Draw a circle with compasses, draw one radius as a starting line, then measure each angle in turn with a protractor.
Label each sector with the item and its angle.

(b)

New books get $35\%$ of $1,300, which is $455.
Furniture gets $30\%$ , which is $390.
The increase is $65, so the percentage increase over furniture is $\frac{65}{390} \times 100 \approx 16.7\%$ , which is $17\%$ to the nearest whole number.
(Straight from the percentages: $\frac{35 - 30}{30} \times 100$ gives the same.)

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