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 2 of 9.
Ayush said:
2 years ago
We got that,
Eq 1: 1/x+4/y=1/15 =>1/x=1/15-4/y.
Eq 2: 1/x+2/y=1/24 =>1/x=1/24-2/y.
Now equate the 1/x values.
i.e 1/15-4/y = 1/24-2/y =>2/y = 1/15-1/24.
So you get y = 80.
By submitting y in the eq 1: 1/x+4/80=1/15 and you get x =60.
X : Y = 60:80 =>3:4.
Eq 1: 1/x+4/y=1/15 =>1/x=1/15-4/y.
Eq 2: 1/x+2/y=1/24 =>1/x=1/24-2/y.
Now equate the 1/x values.
i.e 1/15-4/y = 1/24-2/y =>2/y = 1/15-1/24.
So you get y = 80.
By submitting y in the eq 1: 1/x+4/80=1/15 and you get x =60.
X : Y = 60:80 =>3:4.
(4)
Mathi said:
1 decade ago
Here to solve short cut method....
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
15y+60x=24y+48x
60x-48x=24y-15y
12x=9y
x/y=9/12 --> x/y=3/4
hence 3:4
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
15y+60x=24y+48x
60x-48x=24y-15y
12x=9y
x/y=9/12 --> x/y=3/4
hence 3:4
(1)
Yoonie said:
7 years ago
@D.Rajkumar.
Actually when we say 8.2, the 0.2 there is out of 1 unit or 2 out of 10 or 2 out of 100. There are however 60 minutes in 1 hour which means the same concept cannot be applied since we are calculating out of 60 and not 100. 25/3 is absolutely correct.
Actually when we say 8.2, the 0.2 there is out of 1 unit or 2 out of 10 or 2 out of 100. There are however 60 minutes in 1 hour which means the same concept cannot be applied since we are calculating out of 60 and not 100. 25/3 is absolutely correct.
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)
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)
Juwel said:
6 years ago
It takes 4 hours for 300 km whereof 60 km is covered by train and the rest by car. It takes 20 min more if 100 km is covered by train and rest by car then what is the ration. Please explain.
Sara said:
1 decade ago
Hi @Manisha.
8 is from question see (takes 20 minutes more) than 8 hrs.
So 2 train take 8 hrs 20 minutes.
8 in hour 20 in minutes so convert 20 to hour 20/60.
8(20/60) got it?
8 is from question see (takes 20 minutes more) than 8 hrs.
So 2 train take 8 hrs 20 minutes.
8 in hour 20 in minutes so convert 20 to hour 20/60.
8(20/60) got it?
Anu said:
2 decades ago
Hey as it takes 20mins more for car to travel 200km... then time becomes 8hrs20mins.... so by converting dis time totally into hrs... 8*(20/60)...dis fraction brings u 25/3.
ID.PRASAD said:
8 years ago
@Liton Das.
200/x +400/y = 25/3,
Now, 200 common.
200 (1/x+2/y) = 25/3.
(1/x+2/y) = (25/3) * (1/200),
After the cancellation,
We get,
(1/x+2/y) = 1/24,
Got it.
200/x +400/y = 25/3,
Now, 200 common.
200 (1/x+2/y) = 25/3.
(1/x+2/y) = (25/3) * (1/200),
After the cancellation,
We get,
(1/x+2/y) = 1/24,
Got it.
Deepu said:
1 decade ago
By doing eqn(1) - eqn(2) we can get:
(4/y)-(2/y) = (1/15)-(1/24)
(4y-2y)/y2=(8-5)/120
2y/y2=3/120
2/y=1/40
y=80
By placing y value in eqn(1) we get x = 60.
(4/y)-(2/y) = (1/15)-(1/24)
(4y-2y)/y2=(8-5)/120
2y/y2=3/120
2/y=1/40
y=80
By placing y value in eqn(1) we get x = 60.
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