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Ram started his journey at 9.00 a.m. at 8 km/hour. Hamid started from the same spot in the same direction at 9.30 a.m. at 10 km/hour. Hamid overtakes Ram at ?
11:00 a.m.
12.30 p.m.
12.00 noon
11.30 a.m.
Let the time period at which the Hamid overtakes the Ram x hrs. For Ram, Time at which Ram starts the Journey = 9 a.m. Speed = 8 km/hr. ? Speed = Distance/Time ∴ Distance = Speed × Time ∴ Distance = 8x km.
∴ Distance covered by the Ram in x hours is 8x km. For Hamid, Time at which Hamid Starts the Journey = 9 : 30 a.m.
∴ Difference between the Time of Ram and Hamid = 30 minutes. = 30/60 hrs. = 0.5 hrs.
∴ Time period at which Hamid overtakes Ram = (x - 0.5) hrs.
∴ Distance Covered by the Hamid in the Time Period = 10( x - 0.5) = (10x - 5) km. Now, When Hamid Overtakes Ram, then Both Ram and Hamid will be at the Same Distance,
∴ 8x = 10x - 5 ⇒ 10x - 8x = 5 ⇒ 2x = 5 ⇒ x = 2.5 hrs. ∴ x = 2 hours + 30 minutes. Now, time at which Hamid Overtakes Ram = 9 a.m. + 2 hrs + 30 min. = 11 : 30 a.m.
∴ At 11:30 a.m., Hamid Overtakes Ram.
Hence, option 4 is the correct answer.
By: Amit Kumar ProfileResourcesReport error
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