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:
342 comments Page 7 of 35.
Kishorebabu said:
11 months ago
Convert km/h to m/s.
S(c) = 75000/T -->(1)
S(tr) = 75000/(T-12.5x60)-->(2)
S(tr) = 3/2S(c) -->(3)
Sub (3) in (2).
3/2s(c) = 75000/(T-12.5x60).
sub (1) in above;
(3/2).(75000/T) = 75000/(T-12.5x60).
T = 3x12.5x60 ---->(4)
Sub (4 in (1) [to get the speed of the car].
S(c) = (75000/3x12.5x60 ).(18/5).
s(c) = 120km/h.
S(c) = 75000/T -->(1)
S(tr) = 75000/(T-12.5x60)-->(2)
S(tr) = 3/2S(c) -->(3)
Sub (3) in (2).
3/2s(c) = 75000/(T-12.5x60).
sub (1) in above;
(3/2).(75000/T) = 75000/(T-12.5x60).
T = 3x12.5x60 ---->(4)
Sub (4 in (1) [to get the speed of the car].
S(c) = (75000/3x12.5x60 ).(18/5).
s(c) = 120km/h.
(14)
Smith matsiko said:
1 decade ago
Since the train is 50% faster than than the car and also delayed for 12.5 minutes,
It implies it would have used the time delayed to cover half of the distance=75/2 km.
Therefore its speed =180 km/hr (75/2*60/12.5).
Since trains' speed assuming x to be the speed of the car,
Then x + 0.5x = 180 km,
Thus x = 120 km/hr.
It implies it would have used the time delayed to cover half of the distance=75/2 km.
Therefore its speed =180 km/hr (75/2*60/12.5).
Since trains' speed assuming x to be the speed of the car,
Then x + 0.5x = 180 km,
Thus x = 120 km/hr.
Rahul said:
1 decade ago
It's a very easy question
suppose train running 12.5 min. & lost 12.5 mint in station
s=d/t====>
s=(75/25*60)km/s
s=1/20km/s change in m/sec
s=1000/20 m/sec =50 m/sec
change in km/hr
50*18/5=180km/h train speed.....in option of this question
only 120 car speed 50% is satisfy train speed 120+120/2=180 that's it......
suppose train running 12.5 min. & lost 12.5 mint in station
s=d/t====>
s=(75/25*60)km/s
s=1/20km/s change in m/sec
s=1000/20 m/sec =50 m/sec
change in km/hr
50*18/5=180km/h train speed.....in option of this question
only 120 car speed 50% is satisfy train speed 120+120/2=180 that's it......
GIS said:
1 decade ago
Let Speed of Car = x.
Train is 50% faster than car = x + x/2 = 3x/2.
Time difference = 12. 5 mins = 12. 5/60 hours = 125/600 = 5/24.
Distance = 75 km.
(Distance/Car speed) - (Distance/Train speed) = 12. 5 min = 5/24 hr.
(75/x) - (75/ (3/2x) ) = 5/24.
(75/x) - (150/3x) = 5/24.
25/x = 5/24.
X = (25*24) /5 = 120kmph.
Train is 50% faster than car = x + x/2 = 3x/2.
Time difference = 12. 5 mins = 12. 5/60 hours = 125/600 = 5/24.
Distance = 75 km.
(Distance/Car speed) - (Distance/Train speed) = 12. 5 min = 5/24 hr.
(75/x) - (75/ (3/2x) ) = 5/24.
(75/x) - (150/3x) = 5/24.
25/x = 5/24.
X = (25*24) /5 = 120kmph.
Piyush said:
4 years ago
@All.
So many of us are confused in where the hell this (150x/100) came from right.
So, my simple explanation is that see the train is 50% faster than car.
Now, consider car speed is X so the train speed will be (X+ 50% of X) Now calculate the train speed.
And you will get (X + 50X/100) = 150X/100.
Hope this helps.
So many of us are confused in where the hell this (150x/100) came from right.
So, my simple explanation is that see the train is 50% faster than car.
Now, consider car speed is X so the train speed will be (X+ 50% of X) Now calculate the train speed.
And you will get (X + 50X/100) = 150X/100.
Hope this helps.
(9)
Singh said:
1 decade ago
Here percentage is given means we have to take any unknown quantity as 100 thats why x is taken as 100. here train speed is 50% more than car means it travels with 100+100/2 speed.total speed is 150.now covert 150 into percentages as 150/100.now 150/100=3/2.if car speed is let xkm/h.then train speed is 3/2x km/h.
DevB007 said:
7 years ago
Train speed = 50% faster than car speed.
Train speed = car speed + extra 50 % of car speed.
(car speed = X),
(50% extra of X = X/2),
Train speed = X + X/2 = (X/1 + X/2) = (2X+X)/2;
Train speed = 3X/2.
Train speed = car speed + extra 50 % of car speed.
(car speed = X),
(50% extra of X = X/2),
Train speed = X + X/2 = (X/1 + X/2) = (2X+X)/2;
Train speed = 3X/2.
Deepak porwal said:
1 decade ago
As the train speed is 50% more than car
So train speed is (car speed + 50% of car speed)
i.e. (x+(50/100)*x)= 3x/2;
now time diffrence between them is 12.5 minute
converting it in to hour 12.5/60;
now (distance/speed of train) - (distance /speed of car)= 12.5/60;
as time diffrence between them is 12.5 min;
So train speed is (car speed + 50% of car speed)
i.e. (x+(50/100)*x)= 3x/2;
now time diffrence between them is 12.5 minute
converting it in to hour 12.5/60;
now (distance/speed of train) - (distance /speed of car)= 12.5/60;
as time diffrence between them is 12.5 min;
Vickivignesh said:
8 years ago
speed : car=x;train =y;
x=100% of speed;y=150% of speed; from this wkt, train covers a 150 km per hour but as we know from the detail.
It loses the 12.5 min due to stoppages.so it covers the 150km in 47.5min.
Speed=distance/time.(150*60/47.5)=180kmph.so train speed is 180kmph.
Hence car speed is 120kmph.
x=100% of speed;y=150% of speed; from this wkt, train covers a 150 km per hour but as we know from the detail.
It loses the 12.5 min due to stoppages.so it covers the 150km in 47.5min.
Speed=distance/time.(150*60/47.5)=180kmph.so train speed is 180kmph.
Hence car speed is 120kmph.
Zama said:
7 years ago
@All.
Explanation of this part, 12.5/10 * 60.
12.5 is 125/10.
=> 125/10*60,
=> 5*25/10*60, #since 125 can be written as 5*25.
=> 25/10*12, #after cancelling denominator 60 by numerator 5 as 5*12=60.
=>25/120, #here cancellation goes as 5*5=25 & 5*24=120.
=>5/24.
Hence, we got 5/24.
Explanation of this part, 12.5/10 * 60.
12.5 is 125/10.
=> 125/10*60,
=> 5*25/10*60, #since 125 can be written as 5*25.
=> 25/10*12, #after cancelling denominator 60 by numerator 5 as 5*12=60.
=>25/120, #here cancellation goes as 5*5=25 & 5*24=120.
=>5/24.
Hence, we got 5/24.
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