Aptitude - Time and Distance - Discussion
Discussion Forum : Time and Distance - General Questions (Q.No. 13)
13.
It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:
Answer: Option
Explanation:
Let the speed of the train be x km/hr and that of the car be y km/hr.
| Then, | 120 | + | 480 | = 8  |
1 | + | 4 | = | 1 | ....(i) |
| x | y | x | y | 15 |
| And, | 200 | + | 400 | = | 25 | |
1 | + | 2 | = | 1 | ....(ii) |
| x | y | 3 | x | y | 24 |
Solving (i) and (ii), we get: x = 60 and y = 80.
Ratio of speeds = 60 : 80 = 3 : 4.
Discussion:
84 comments Page 9 of 9.
Ria said:
11 months ago
How did 8 come in solution?
Please explain me.
Please explain me.
(11)
Hemalatha said:
9 months ago
Let the speed af the train be T and car be C.
The time taken by train and car is:
120/T+480/C=8hrs is equation 1
200/T+400/C=8hrs 20 mins which is 200/T+400/C=25/3 is equation 2
Multiply equation (1)by 5 and equation (2) by 3 to cancel the fractions;
Therefore,
600/T+2400/C = 40
600/T+1200/C = 25
Now subtract equation (1) and (2);
Therefore,
(600/T + 2400/C = 40) - (600/T + 1200/C = 25).
1200/C = 15,
C = 1200/15,
C = 80.
Substitute C = 80 in equation (1)
600/T + 2400/80 = 40,
600/T = 40 - 2400/80.
600/T = 800/80,
T = 600/10.
T = 60.
So the ratio for train and car would be:
60:80
Therefore the ratio is 3:4.
The time taken by train and car is:
120/T+480/C=8hrs is equation 1
200/T+400/C=8hrs 20 mins which is 200/T+400/C=25/3 is equation 2
Multiply equation (1)by 5 and equation (2) by 3 to cancel the fractions;
Therefore,
600/T+2400/C = 40
600/T+1200/C = 25
Now subtract equation (1) and (2);
Therefore,
(600/T + 2400/C = 40) - (600/T + 1200/C = 25).
1200/C = 15,
C = 1200/15,
C = 80.
Substitute C = 80 in equation (1)
600/T + 2400/80 = 40,
600/T = 40 - 2400/80.
600/T = 800/80,
T = 600/10.
T = 60.
So the ratio for train and car would be:
60:80
Therefore the ratio is 3:4.
(5)
Siva B said:
8 months ago
@All.
Here is my explanation.
120/x - 480/y = 8
by taking 120 commons we get
1/x - 4/y = 8/120,
1/x -4/y = 1/15 ---> (1)
200/x - 400/y = 8+20/60
min so div by 60.
By taking common 200 we get
1/x - 2/y = 1/24
Solving both equations.
1/x + 4/y = 1/15 --> (1)
1/x + 2/y = 1/24 --> (2)
By subtracting (1),(2)
4/y -2/y = 1/15 - 1/24,
2/y = 8-5/120,
2/y = 1/40,
Y = 80.
Sub y = 80 in eq (1)
X = 60
Therefore x : y.
60:80 div by 2,
And finally answer = 3:4 we get.
Here is my explanation.
120/x - 480/y = 8
by taking 120 commons we get
1/x - 4/y = 8/120,
1/x -4/y = 1/15 ---> (1)
200/x - 400/y = 8+20/60
min so div by 60.
By taking common 200 we get
1/x - 2/y = 1/24
Solving both equations.
1/x + 4/y = 1/15 --> (1)
1/x + 2/y = 1/24 --> (2)
By subtracting (1),(2)
4/y -2/y = 1/15 - 1/24,
2/y = 8-5/120,
2/y = 1/40,
Y = 80.
Sub y = 80 in eq (1)
X = 60
Therefore x : y.
60:80 div by 2,
And finally answer = 3:4 we get.
(9)
Jashanpreet singh said:
1 month ago
train : car = time
120 : 480 = 8hr.
200 : 400 = 8hr 20min.
So, 80km =20min more by train.
480km dist. by train in 2hr.
Then the speed of the train is 60k/h,
Total time 8hr.
8 - 2 = 6hr.
Car speed = 480/6 =80.
T:C = 60:80.
= 3:4.
120 : 480 = 8hr.
200 : 400 = 8hr 20min.
So, 80km =20min more by train.
480km dist. by train in 2hr.
Then the speed of the train is 60k/h,
Total time 8hr.
8 - 2 = 6hr.
Car speed = 480/6 =80.
T:C = 60:80.
= 3:4.
(2)
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