Points P, Q, R, S and T lie in that order on a straight path. The ratio of QR to PR is 3 : 5. The ratio of QR to QS is 3 : 4. QS is half of QT. PT is 150 m. What is the length of ST?
- 30 m
- 60 m
- 90 m
- 120 m
Need a hint?
Measure every distance from P in the same units, and use the 'half of QT' link to find where T is before you convert to metres.
Worked answer
- Take QR = 3 units, so PR = 5 units and PQ = 2 units.
- QS = 4 units, so S is 2 + 4 = 6 units from P.
- QT = 2 × QS = 8 units, so T is 2 + 8 = 10 units from P.
- PT = 10 units = 150 m, so 1 unit = 15 m.
- ST = 10 − 6 = 4 units = 4 × 15 = 60 m.
Answer: 60 m
The mistake this question tests
Habit
Stopped at one part in ratio
Many pupils take QS as the whole of QT, or stop at the ratio part without finding where S and T sit, so they pick a wrong multiple of the unit.
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See the answer →Practise PSLE ratio until the mistakes stop.
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