Problem 15 · 2019 Math Kangaroo
Hard
Geometry & Measurement
proportionspatial-reasoning
The system shown consists of three pulleys connected to each other by two ropes. The end P of one rope is pulled down by 24 cm. By how many centimetres does point Q move upwards?
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Answer: D — 6
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Hint 1 of 2
With movable pulleys the total rope length is conserved; the 24 cm pulled at P is shared among the rope segments that support each pulley.
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Hint 2 of 2
Follow each rope over its pulleys and see how the displacement is divided down to point Q.
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Approach: conserve rope length across the pulley system
- Pulling P down by 24 cm feeds slack into the connected ropes.
- Each movable pulley halves the displacement passed on, and the two ropes combine the reductions before reaching Q.
- Following the displacement through the system, Q rises by 6 cm.
- Answer (D) 6.
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