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 17 of 36.
Soham said:
9 years ago
Many have asked how 3/2x came?
According to me "train travels 50% faster than car"
Let the speed of car be x.
Then the speed of train is,
The speed of car+ 50%speed of car (as per question)
ie,
x+ 1/2x.
=3/2x.
According to me "train travels 50% faster than car"
Let the speed of car be x.
Then the speed of train is,
The speed of car+ 50%speed of car (as per question)
ie,
x+ 1/2x.
=3/2x.
Gurbir said:
9 years ago
Train and car covers the same distance in same time. But train 50%faster than the car.
The Train stops at stations 12.5.
It means they cover 75km in 25minutes.
So convert minutes into hr (75÷60=12/5).
So that the speed of the train = 75*12÷5=180,
50% of 120 is 60,
180 - 60 = 120.
So Speed of car is 120km/hr.
Because train is faster than car 50% is given above.
The Train stops at stations 12.5.
It means they cover 75km in 25minutes.
So convert minutes into hr (75÷60=12/5).
So that the speed of the train = 75*12÷5=180,
50% of 120 is 60,
180 - 60 = 120.
So Speed of car is 120km/hr.
Because train is faster than car 50% is given above.
Shakeeb said:
9 years ago
***Assume the speed of car be 'a'.
TIME OF THE CAR = distance of car/speed of car.
= 75/a.
Since train is 50% faster than car, therefore
50% of a=====50/100 X a===1/2 X a====a/2 (this is 50% of the car speed),
a + a/2====3a/2 (train is 50% faster than car).
TIME OF THE TRAIN = distance of train/speed of train.
= 75/(3a/2),
= 150/3a,
= 50/3a.
Time of the car - time of the train = 12.5 min ----------------------> MAIN FORMULA.
75/a - 150/3a = 12.5/60 (since we are calculating in km/hr, so divide it by 60),
75/a - 50/a = 12.5/60,
= 120.
TIME OF THE CAR = distance of car/speed of car.
= 75/a.
Since train is 50% faster than car, therefore
50% of a=====50/100 X a===1/2 X a====a/2 (this is 50% of the car speed),
a + a/2====3a/2 (train is 50% faster than car).
TIME OF THE TRAIN = distance of train/speed of train.
= 75/(3a/2),
= 150/3a,
= 50/3a.
Time of the car - time of the train = 12.5 min ----------------------> MAIN FORMULA.
75/a - 150/3a = 12.5/60 (since we are calculating in km/hr, so divide it by 60),
75/a - 50/a = 12.5/60,
= 120.
Ravikumar J said:
9 years ago
Good explanation, thank you @Rihan.
Suvasish Singha said:
9 years ago
Let, Speed of the train be X kmph.
Than, Speed of the train= x + (x * 50/100).
= x + x/2,
= (2x+x) / 2,
= 3x/2.
Than, Speed of the train= x + (x * 50/100).
= x + x/2,
= (2x+x) / 2,
= 3x/2.
Chirag Painter said:
9 years ago
Let speed ratio=car:train=100:150=2:3.
Here distance is same so as per the rule "if distance is same then speed ratio is inversely proportional to time"
Speed ratio = 2:3
Time ratio = 3:2
Therefore car usual time = 3 * 12.5 = 37.5 min.
And train usual time = 2 * 12.5 = 25 min.
Now, speed of car = Distance/time,
= 75kmph / 37.5 min,
= 2.
Now convert into hour=2 * 60 = 120kmphr.
Here distance is same so as per the rule "if distance is same then speed ratio is inversely proportional to time"
Speed ratio = 2:3
Time ratio = 3:2
Therefore car usual time = 3 * 12.5 = 37.5 min.
And train usual time = 2 * 12.5 = 25 min.
Now, speed of car = Distance/time,
= 75kmph / 37.5 min,
= 2.
Now convert into hour=2 * 60 = 120kmphr.
Sanju said:
9 years ago
Good explanation, thanks @Raihan.
Nng said:
9 years ago
Hi, can you please explain why we are subtracting the time of car and train to get 12.5 minutes?
Madhu said:
9 years ago
@Bdboy Hasan.
How do you say car's speed is 3x?
How do you say car's speed is 3x?
Raihan Bangladesh said:
9 years ago
Let, car speed = X km/min.
Train speed = X + x* (50/100) Km/min.
=X+X/2 km/min.
=3X/2 km/min.
Time of car t =75/X.
Time of Train t =75/ (3X/2).
According to the question.
75/X=75/ (3X/2) +12. 5.
>> 75/X-150/3X=12. 5.
>> (225-150) /3X=12. 5.
>> 75 = 37. 5X.
>> X = 2 Km/min.
So car speed 1 minute to 2 km.
Car Speed 60 minutes to (60*2) = 120 km/h.
Train speed = X + x* (50/100) Km/min.
=X+X/2 km/min.
=3X/2 km/min.
Time of car t =75/X.
Time of Train t =75/ (3X/2).
According to the question.
75/X=75/ (3X/2) +12. 5.
>> 75/X-150/3X=12. 5.
>> (225-150) /3X=12. 5.
>> 75 = 37. 5X.
>> X = 2 Km/min.
So car speed 1 minute to 2 km.
Car Speed 60 minutes to (60*2) = 120 km/h.
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