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17 Jan 2023, 10:00
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A
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Difficulty:
85%
(hard)
Question Stats:
53% (03:05) correct
47%
(03:25)
wrong
based on 53
sessions
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John leaves from his home at 10 AM and starts driving towards a city that is 300 kilometres away, at a constant speed of 50 miles per hour. His brother Martin leaves the home at 11:30 AM and starts driving on the same route at a constant speed of 60 miles per hour. If they stop driving once they reach the city, which of the following statements must be true? (1 mile = 1.6 kilometres)
I. John reaches the city before Martin
II. At 1:30 PM, John is 55 kilometres ahead of Martin
III. Martin overtake John at 4 PM
A. I only
B. II only
C. III only
D. I and II only
E. II and III only
I. John reaches the city before Martin
II. At 1:30 PM, John is 55 kilometres ahead of Martin
III. Martin overtake John at 4 PM
A. I only
B. II only
C. III only
D. I and II only
E. II and III only
21 Jan 2023, 00:40
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Bunuel
Distance travelled by John between 10 am and 11:30 m =
1.5 * 1.6 * 50 = 120 kilometers
Distance remaining from destination = 180 kilometers
Time that John will take to cover the remaining 180 kilometers = \(\frac{180 }{ 50 * 1.6} \) = 2.25 hours
Time Martin will take to cover the gap of 120 kilometers =
\(\frac{120 }{ (60 - 50) * 1.6}\) = 7.5 hours
As Martin takes more time to cover the gap than John takes to reach the destination, it is not possible that Matin will ever overtake John.
So III is ruled out.
I is correct as John reaches earlier than Martin.
II is also incorrect, it will 7.5 hours for Martin to cover a gap of 120 kms. Hence in two hours he cannot be 55 miles behind John.
Option A
