A car workshop's technician logs how a typical 8-hour working day divides between servicing, MOT tests and general repairs. The pie chart shows this split, ...
Question 1 Report
A car workshop's technician logs how a typical 8-hour working day divides between servicing, MOT tests and general repairs. The pie chart shows this split, with the angle of each sector given in degrees.
- Show that the ratio of time spent on servicing to MOT tests to repairs is \(2 : 1 : 1\). (1)
- Given that the technician works an 8-hour day, work out the number of hours spent on each activity. (3)
Answer Details
This question tests converting angles on a pie chart into a ratio, and then using that ratio to share a total time.
(a) A full circle is \( 360^\circ \), and each degree represents the same fraction of the day. Dividing all three angles by their common factor of 90 gives
\[ 180 : 90 : 90 = 2 : 1 : 1 \] [1 mark]
(b) The 8-hour day is now shared in the ratio \( 2 : 1 : 1 \), which has \( 2 + 1 + 1 = 4 \) parts. One part is
\[ 8 \div 4 = 2 \text{ hours} \] [1 mark]
Servicing takes 2 parts, so \( 2 \times 2 = 4 \) hours. [1 mark] MOT tests and repairs each take 1 part, so each takes \( 1 \times 2 = 2 \) hours. [1 mark]
As a check, \( 4 + 2 + 2 = 8 \) hours, which matches the length of the working day; converting the angles to a ratio first avoids having to work with degrees throughout.
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