Maths Puzzles for KS3/KS4

Puzzling taxi fares


Teaching notes

The best way to introduce this is to ask students what is fair when sharing a taxi. The fundamental principle that they should arrive at is that the fare should be shared equally when there is multiple occupancy of the taxi, but any distance when there is sole occupancy should be the sole occupant’s responsibility.

For the purposes of this puzzle, one has to assume that the fare is proportional to the distance travelled, ie there is no set hire charge added on at the beginning of the journey.


Based on the principle outlined above, for the first 10 km A and B share the 10 fare, paying 5 each. Then B continues on the journey and pays the remaining 10 himself. In total, A pays 5 (a quarter of the total) and B pays 15 (three quarters of the total).


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