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A train can travel 50% faster than a car. Both start from point A at t

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A train can travel 50% faster than a car. Both start from point A at t  [#permalink]

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New post 20 Sep 2019, 23:17
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A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:
A. 100 kmph
B. 110 kmph
C. 120 kmph
D. 130 kmph
E. 230 kmph
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Re: A train can travel 50% faster than a car. Both start from point A at t  [#permalink]

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New post 21 Sep 2019, 00:33
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dharam44 wrote:
A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:
A. 100 kmph
B. 110 kmph
C. 120 kmph
D. 130 kmph
E. 230 kmph


Let speed of car is v
Speed of train is 50% more than the car = 1.5 * v
Distance traveled by both of them is 75km each.
Since both start at the same time and reach at the same time so time taken by both of them will be same.

Time take by Car = time taken by train
75/v = 75/1.5v + 12.5 (as train stopped in between for 12.5mins) (calculating speed in km/min)

75/v - 75/1.5v = 12.5
75/v ( 1 - 1/1.5) = 12.5
75/v ( (1.5-1)/1.5) = 12.5
75/v * 0.5/1.5 = 12.5
75/v = 12.5 * 1.5/0.5
75/v = 12.5*3 = 37.5
v = 75/37.5 = 2 km/min
= 2*60 km/hr (as 1min = 1/60 hr)
= 120 km/hr
So, answer is C

Hope it helps!
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Re: A train can travel 50% faster than a car. Both start from point A at t  [#permalink]

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New post 21 Sep 2019, 01:03
Let, Speed of Car be x. Thus, speed of train = 1.5x

Let time taken by car to travel 75km be T1

Thus, 75/x = T1

Train reaches in the same time, however takes a break of 12.5 min

Thus, 75/1.5x + 12.5 = T1

Equating both the eqns;

75/x = 75/1.5x + 12.5

75/x - 50/x = 12.5

25/x = 12.5

Thus, x = 20km/min

Options are in kmph

Hence, x= 20× 60= 120kmph

Option, C.

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Re: A train can travel 50% faster than a car. Both start from point A at t  [#permalink]

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New post 21 Sep 2019, 03:46
3V/2(t - 12.5/60)=Vt
t/2=12.5/40
t=25/40
So,25/40× V=75
--》V=120kmph
Option C

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Re: A train can travel 50% faster than a car. Both start from point A at t   [#permalink] 21 Sep 2019, 03:46
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