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:
350 comments Page 8 of 35.
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.
ANom said:
3 months ago
Speed of car =2/3 the speed of the train.
ie Vc=2/3 Vt, therefore,
Time taken by car =3/2 Time taken by train ie.Tc=3/2 Tt.
Also,
Tc = Tt+15/60 hr ie. Tc = Tt + 1/4.
Therefore:
3/2 Tt = Tt+1/4
Tt = 1/2 = 0.5 hr.
Therefore, Tc = 0.75 = hr.
Distance = v x t.
75 km = Vc x 0.75,
Vc = 100km
Vt = 120.
ie Vc=2/3 Vt, therefore,
Time taken by car =3/2 Time taken by train ie.Tc=3/2 Tt.
Also,
Tc = Tt+15/60 hr ie. Tc = Tt + 1/4.
Therefore:
3/2 Tt = Tt+1/4
Tt = 1/2 = 0.5 hr.
Therefore, Tc = 0.75 = hr.
Distance = v x t.
75 km = Vc x 0.75,
Vc = 100km
Vt = 120.
(3)
Aishwarya said:
6 years ago
Let the Speed of car be=x km/hr.
Speed of train = 1.5x km/hr.
Time taken by car to travel 75km = 75/x h.
Time taken by train to travel 75 km = 75/1.5 x-12.5/60.
Both are equal.
75/x = 75/1.5x-12.5/60.
1/x(75"75/1.5) = 12.5/60.
25/x = 12.5/60
1500 = 12.5x.
So, x = 1500/12.5 = 120 km/hr is the Answer.
Speed of train = 1.5x km/hr.
Time taken by car to travel 75km = 75/x h.
Time taken by train to travel 75 km = 75/1.5 x-12.5/60.
Both are equal.
75/x = 75/1.5x-12.5/60.
1/x(75"75/1.5) = 12.5/60.
25/x = 12.5/60
1500 = 12.5x.
So, x = 1500/12.5 = 120 km/hr is the Answer.
Jinto said:
1 decade ago
Can anybody explain if both the vehicle reaches at the same time then where is the delay arises i am talking about if two vehicles reaches at the same time then how this equation came
(75/x)-(75/(3/2)x)=12.5/60, 12.5 minutes delay will not be ther if both the vehicles reaches at the same time pls help
(75/x)-(75/(3/2)x)=12.5/60, 12.5 minutes delay will not be ther if both the vehicles reaches at the same time pls help
Justin said:
1 decade ago
Hi @Mancy,
OK here the answer for your question,
Ex:1% of 2 = 1/100*2 = 1/50.
10% of 100 = 10/100*100 = 10.
So now come to our problem ok.
Take speed of the car is X ok. (Consider 100).
Train is 50% faster ok so 100+50 = 150;.
So we need find that 150%X which gives 150/100*X.
All the best.
OK here the answer for your question,
Ex:1% of 2 = 1/100*2 = 1/50.
10% of 100 = 10/100*100 = 10.
So now come to our problem ok.
Take speed of the car is X ok. (Consider 100).
Train is 50% faster ok so 100+50 = 150;.
So we need find that 150%X which gives 150/100*X.
All the best.
Sai Durga said:
2 years ago
Let the speed of the train be x.
So, train speed 50% faster than car means x + x/2 = 3x/2, speed = 75km/hr,
Time delayed = 12.5 mins = 12.5/60 sec.
Now;
D/s = T; (here speed = speed of the car -speed of the train),
So,
75/x -75/3x/2 = 12.5/60.
75/x - 50/x = 5/24.
x = 25 x 24/5.
x = 120 km/hr.
So, train speed 50% faster than car means x + x/2 = 3x/2, speed = 75km/hr,
Time delayed = 12.5 mins = 12.5/60 sec.
Now;
D/s = T; (here speed = speed of the car -speed of the train),
So,
75/x -75/3x/2 = 12.5/60.
75/x - 50/x = 5/24.
x = 25 x 24/5.
x = 120 km/hr.
(13)
Neranjan said:
7 years ago
A to B have 75km.
We think, Train not stopped,
It can go 112.5km.
So, train speed =112.5km-75km/12.5m.
12.5m covert to hour 12.5/60.
= 37.5km * 60/12.5,
= 180kmph.
So car speed =180kmph * 100/150.
=120kmph.
We think, Train not stopped,
It can go 112.5km.
So, train speed =112.5km-75km/12.5m.
12.5m covert to hour 12.5/60.
= 37.5km * 60/12.5,
= 180kmph.
So car speed =180kmph * 100/150.
=120kmph.
Sai Durga said:
2 years ago
Let the speed of the train be x.
So, train speed 50% faster than car means x + x/2 = 3x/2, speed = 75km/hr,
time delayed = 12.5 mins==12.5/60 sec.
Now;
D/s = T; (here speed = speed of the car -speed of the train),
So,
75/x -75/3x/2 = 12.5/60.
75/x - 50/x = 5/24.
x = 25 x 24/5
x = 120 km/hr.
So, train speed 50% faster than car means x + x/2 = 3x/2, speed = 75km/hr,
time delayed = 12.5 mins==12.5/60 sec.
Now;
D/s = T; (here speed = speed of the car -speed of the train),
So,
75/x -75/3x/2 = 12.5/60.
75/x - 50/x = 5/24.
x = 25 x 24/5
x = 120 km/hr.
(29)
Sreekanth said:
1 decade ago
Think... Y 3/2x came with an example...
if u think car has x speed, then train ll have 2x.
then substitute x with simple value..
x:2x
if x=10 then
10:20
it mean train has double value of car speed.
but x:3/2x
then 10:15x
In which train has 50% faster than car.
50% of car is 5. so 10+5=15.
if u think car has x speed, then train ll have 2x.
then substitute x with simple value..
x:2x
if x=10 then
10:20
it mean train has double value of car speed.
but x:3/2x
then 10:15x
In which train has 50% faster than car.
50% of car is 5. so 10+5=15.
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