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Distance between two stations X and Y is 220 km. Trains P and Q leave station X at 8 a.m. and 9.51 a.m. respectively at the speed of 25 kmph and 20 kmph respectively for journey towards Y. A train R leaves station Y at 11.30 a.m. at a speed of a 30 kmph. for journey towards X. When will P be at equal distance from Q and R ?
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- 12:48 pm.
- 12:30 pm.
- 12:45 pm.
- 11:48 pm.
Correct Option: A
Distance covered by P till 11.30 a.m.
= (11.30 a.m. – 8 a.m.) × 25km
| = 3 | × 25 = 87.5 km. | |
| 2 |
Distance covered by Q till 11.30 a.m.
= (11.30 – 9.51 am) × 20
| = 1 | hrs. × 20 = 33 km | |
| 60 |
So, at 11.30 a.m. the three trains will be at positions shown below :
P gains 5 km every hour over Q.
Relative speed of P w.r.t. R = 20 + 30 = 50 km per hr
Let P be at equal distance from Q and R after t hours.
∴ (87.5 – 33) + 5t
= 132.5 –55t
or, 54.5 + 5t = 132.5 – 55t
or, 60 t = 78
| or, t = | hrs. | |
| 60 |
= 1 hr 18 minutes
11.30 am + 1 hr. 18 min.
= 12.48 pm
At 12.48 pm, P would have covered a distance
= (12.48 pm – 8 am) × 25
= 120 km
Therefore, P will be at equal distance from Q and R at 12.48 pm
