Aptitude - Time and Distance - Discussion
Discussion Forum : Time and Distance - General Questions (Q.No. 4)
4.
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:
Answer: Option
Explanation:
Let speed of the car be x kmph.
| Then, speed of the train = | 150 | x | = |  |
3 | x |  kmph. |
| 100 | 2 |
 |
75 | - | 75 | = | 125 |
| x | (3/2)x | 10 x 60 |
 |
75 | - | 50 | = | 5 |
| x | x | 24 |
| x = |
|
25 x24 | |
= 120 kmph. |
| 5 |
Discussion:
351 comments Page 36 of 36.
SutharsanBabu said:
1 day ago
Most Members doubt is how come this speed equation =(3/2)x.
speed =x.
Eg 1:
Car speed =50.
Train speed =>50 + (50/2)=> 50 + 25 = 75
Speed equation => train speed/car speed => 75/50 =3/2.
Ex 2:
Car speed =100.
Train speed =>100+(100/2) => 100 + 50 = 150.
Speed equation =>train speed/car speed => 150/100 = 3/2.
Time equation for train:
However, the train lost about 12.5 minutes while stopping at the stations.
Train's Total Time = Run time + Stopping time.
Convert 12.5 minutes in Hours as follows by 12.5 => 12.5/60 => 125/600 => 25/120 = 5/24.
Want to find the real speed of both the car and the train:
Formula : time = distance/speed.
speed = x.
car = train.
75/x = 75/(3/2)x + 5/24 simplify ->(75/1)*(2/3)->150/3=50/1.
75/x = 50/1x + 5/24 -> 1x and x both are same.
(75/x)-(50/x) = 5/24.
75-50/x = 5/24.
25x = 5/24.
x = 5/24/25, simplify -> (24*25)/5 -> 600/5 -> 120/1.
x= 120/1, don't consider 1.
Answer = 120.
speed =x.
Eg 1:
Car speed =50.
Train speed =>50 + (50/2)=> 50 + 25 = 75
Speed equation => train speed/car speed => 75/50 =3/2.
Ex 2:
Car speed =100.
Train speed =>100+(100/2) => 100 + 50 = 150.
Speed equation =>train speed/car speed => 150/100 = 3/2.
Time equation for train:
However, the train lost about 12.5 minutes while stopping at the stations.
Train's Total Time = Run time + Stopping time.
Convert 12.5 minutes in Hours as follows by 12.5 => 12.5/60 => 125/600 => 25/120 = 5/24.
Want to find the real speed of both the car and the train:
Formula : time = distance/speed.
speed = x.
car = train.
75/x = 75/(3/2)x + 5/24 simplify ->(75/1)*(2/3)->150/3=50/1.
75/x = 50/1x + 5/24 -> 1x and x both are same.
(75/x)-(50/x) = 5/24.
75-50/x = 5/24.
25x = 5/24.
x = 5/24/25, simplify -> (24*25)/5 -> 600/5 -> 120/1.
x= 120/1, don't consider 1.
Answer = 120.
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