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:
345 comments Page 19 of 35.
Rahul said:
8 years ago
@Jignesh.
Time is given in minutes. So to change it in hours, it is divided by 60.
And 10 has been placed for the decimal point.
Time is given in minutes. So to change it in hours, it is divided by 60.
And 10 has been placed for the decimal point.
Raihan Bangladesh said:
8 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.
(1)
Madhu said:
8 years ago
@Bdboy Hasan.
How do you say car's speed is 3x?
How do you say car's speed is 3x?
Nng said:
8 years ago
Hi, can you please explain why we are subtracting the time of car and train to get 12.5 minutes?
Sanju said:
8 years ago
Good explanation, thanks @Raihan.
Chirag Painter said:
8 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.
Suvasish Singha said:
8 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.
Ravikumar J said:
8 years ago
Good explanation, thank you @Rihan.
Shakeeb said:
8 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.
Gurbir said:
8 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.
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