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 3 of 9.
Kavitha said:
1 decade ago
This problems in last step step cannot do understand?
Santosh said:
1 decade ago
Please any one explain how 1/24 comes?
Moumita roy said:
1 decade ago
I can't understand to 1/x +4/y =1/15 and 1/x +2/y =1st/24.
Then how will do x=60 y=80?
Then how will do x=60 y=80?
Ophi said:
1 decade ago
The first equation is:
(120/x)+(480/y) = 8.
120[(1/x)+(4/y)] = 8.
(1/x)+(4/y) = 8/120.
(1/x)+(4/y) = 1/15.
Similarly in the second eqn:
(200/x)+(400/y) = 25/3.
200[(1/x)+(2/y)] = 25/3.
(1/x)+(2/y) = 25/(3*200).
(1/x)+(2/y) = 1/24.
Now you want to equate both the equations so try and get the common values of xy for both equations.
1/x+4/y = 1/15 --> take xy as multiples.
(y+4x)/xy = 1/15 --> take 15 to left hand side.
15y + 60x = xy.
Similarly,
1/x+2/y = 1/24.
24y+48x = xy.
Now easy to equate, substitute value of xy.
15y+60x = 24y+48x.
60x-48x = 24y-15y.
12x = 9y.
x/y = 9/12 --> x/y = 3/4.
Hence 3:4.
(120/x)+(480/y) = 8.
120[(1/x)+(4/y)] = 8.
(1/x)+(4/y) = 8/120.
(1/x)+(4/y) = 1/15.
Similarly in the second eqn:
(200/x)+(400/y) = 25/3.
200[(1/x)+(2/y)] = 25/3.
(1/x)+(2/y) = 25/(3*200).
(1/x)+(2/y) = 1/24.
Now you want to equate both the equations so try and get the common values of xy for both equations.
1/x+4/y = 1/15 --> take xy as multiples.
(y+4x)/xy = 1/15 --> take 15 to left hand side.
15y + 60x = xy.
Similarly,
1/x+2/y = 1/24.
24y+48x = xy.
Now easy to equate, substitute value of xy.
15y+60x = 24y+48x.
60x-48x = 24y-15y.
12x = 9y.
x/y = 9/12 --> x/y = 3/4.
Hence 3:4.
(1)
Srijan said:
1 decade ago
How it comes 25/3 please explain?
Sukanya said:
1 decade ago
Convert 20 minutes into hrs, 20/60 = 1/3 hrs.
Since it s 20 minutes more than the 8 hrs,
Total time = (1/3)+8 = 25/3 hrs.
Since it s 20 minutes more than the 8 hrs,
Total time = (1/3)+8 = 25/3 hrs.
Satish said:
1 decade ago
(200/x)+(400/y) = 8+(20/60).
=> 200(1/x+2/y) = 25/3.
=> 1/x+2/y = 25/(3*200).
By cancellation we get,
1/x+2/y = 1/24.
=> 200(1/x+2/y) = 25/3.
=> 1/x+2/y = 25/(3*200).
By cancellation we get,
1/x+2/y = 1/24.
Rakesh said:
1 decade ago
Do we any alternative method for this because this method is time consuming.
Rajani said:
1 decade ago
I have tried putting y as 5 in both the equation but it is not giving x as 60. Please explain.
Manisha said:
1 decade ago
How this 8 value came in equation any one can you please explain?
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