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    				| 1. | Robert is travelling on his cycle and has calculated to reach point A at 2 p.m. if he travels at 10 km/hr, he will reach there at 12 noon if he travels at 15 km/hr. At what speed must he travel to reach A at 1 p.m.?(a) 8 km/hr (b) 11 km/hr (c) 12 km/hr (d) 14 km/hr | 
| Answer» (c) 12 km/hr Let the distance travelled be x km. Then \(\frac{x}{10}-\frac{x}{15}\) = 2 ⇒ 3x – 2x = 60 ⇒ x = 60 km Time taken to travel 60 km at 10 km/hr = \(\big(\frac{60}{10}\big)\) hrs = 6 hrs. So Robert started 6 hours before 2 P.M., i.e., at 8 P.M. ∴ Speed required to reach A at 1 P.M. = \(\big(\frac{60}{5}\big)\) km/hr = 12 km/hr. | |