## Exam-Style Question on Proportion## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 161. This question is similar to one that appeared on a GCSE Higher paper (specimen) for 2017. The use of a calculator is not allowed.

The Billing triplets are planting seedlings on the first day of the month. The three of them take two hours to plant 300 seedlings.

(a) On the second day of the month the triplets are joined by their friend Billy who helps them. Working at the same rate, how many plants should the four of them be able to plant in two hours?

(b) Working at the same rate, how much longer would it take four people to plant 1000 seedlings than it would take five people?

(c) Billy says that it took two hours for three people to plant 300 seedlings. If I assume they work all day, then in one day three people will plant 3600 seedlings because 300 × 12 = 3600.

Why is Billy's assumption not reasonable? What effect has Billy's assumption had on his answer?

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