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NEET Physics QUESTION #1039
Question 1
Two cities X and Y connected by buses every T min. A girl on scooter at 60 km/h sees buses every 30 min in her direction and every 10 min opposite. Period T and bus speed:
  • 10 min, 90 km/h
  • 15 min, 120 km/h✔️
  • 9 min, 40 km/h
  • 25 min, 100 km/h
Correct Answer Explanation
Let bus speed \(=v\), period \(=T\). Relative speed with girl (same direction): \(v-60\). Buses come every 30 min: \(\frac{vT}{v-60}=30\). Opposite direction: \(\frac{vT}{v+60}=10\). Dividing: \(\frac{v+60}{v-60}=3\Rightarrow v+60=3v-180\Rightarrow v=120\ \text{km/h}\). Then \(T=\frac{10(120+60)}{120}=15\ \text{min}\).