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 7 of 9.
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)
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?
Santosh said:
1 decade ago
Please any one explain how 1/24 comes?
Kavitha said:
1 decade ago
This problems in last step step cannot do understand?
Ravichandran.k said:
1 decade ago
@Darshan kumar,
That car take more 20 min so 8.20 mins.
8+20/60= 8+1/3 = 8*3+1=24/3 is come.
That car take more 20 min so 8.20 mins.
8+20/60= 8+1/3 = 8*3+1=24/3 is come.
Darshan Kumar said:
1 decade ago
Hi , Any one can tell me in detail how 25/3 came ?
Prasad said:
1 decade ago
Train speed = 80/20*60 = 240km.
Car speed = 600-240 = 360km.
Ratio 240:360 or 3:4.
Car speed = 600-240 = 360km.
Ratio 240:360 or 3:4.
(1)
Sagar said:
1 decade ago
Hi @kamal,
To solve the equation 1 and 2 easily we had taken 120, 200 common from equations.
To solve the equation 1 and 2 easily we had taken 120, 200 common from equations.
Kamal said:
1 decade ago
Please explain how 1/15 and 1/24 comes ?
Rajeshwari said:
1 decade ago
Hi kishore,
The first eqn 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
The first eqn 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
(1)
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