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To travel 816 km, an Express train takes 9 hours more than Rajdhani train. If however, the speed of the Express train is doubled, it takes 4 hours less than Rajdhani train. What is the speed of Rajdhani train?
- a)48 km/hr
- b)62.8 km/hr
- c)33.2 km/hr
- d)77.5 km/hr
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
To travel 816 km, an Express train takes 9 hours more than Rajdhani tr...
Let time taken by Rajdhani be t
⇒ Time taken by Express train = t + 9
Speed = Distance/Time
⇒ 408(t + 9) = 816(t - 4)
⇒ 408t = 6936
⇒ t = 17 hr
∴ Speed of Rajdhani = 816/17 = 48 km/hr
⇒ Time taken by Express train = t + 9
Speed = Distance/Time
⇒ 408(t + 9) = 816(t - 4)
⇒ 408t = 6936
⇒ t = 17 hr
∴ Speed of Rajdhani = 816/17 = 48 km/hr
Most Upvoted Answer
To travel 816 km, an Express train takes 9 hours more than Rajdhani tr...
Solution:
Let the speed of Rajdhani train be x km/hr.
Then, the speed of Express train is 2x km/hr (since it is doubled).
Time taken by Rajdhani train to travel 816 km = 816/x hours
Time taken by Express train to travel 816 km = (816/2x) hours
According to the given condition, Express train takes 9 hours more than Rajdhani train, so:
(816/2x) = (816/x) + 9
Multiplying both sides by 2x, we get:
816 = 2(816) + 9x
9x = 816 - 2(816) = -816
x = -816/9 = -90.67
This is not a possible speed, so we can conclude that our assumption that Rajdhani train is slower than Express train is incorrect.
Now, according to the second condition, when the speed of Express train is doubled, it takes 4 hours less than Rajdhani train, so:
816/x - 4 = 816/(2x)
Multiplying both sides by 2x, we get:
1632 - 4x = 816
4x = 816 - 1632 = -816
x = -816/4 = -204
Again, this is not a possible speed, so we need to flip our assumption and assume that Rajdhani train is actually faster than Express train.
Let the speed of Rajdhani train be y km/hr (where y is greater than 0).
Then, the speed of Express train is 2y km/hr.
Now, we can use the same equations as before:
(816/2y) = (816/y) + 9
Multiplying both sides by 2y, we get:
816 = 2(816) + 18y
18y = 816 - 2(816) = -816
y = -816/18 = -45.33
Again, this is not a possible speed, so we can conclude that our assumption that Rajdhani train is faster than Express train is also incorrect.
Therefore, there is no valid solution to this problem.
Let the speed of Rajdhani train be x km/hr.
Then, the speed of Express train is 2x km/hr (since it is doubled).
Time taken by Rajdhani train to travel 816 km = 816/x hours
Time taken by Express train to travel 816 km = (816/2x) hours
According to the given condition, Express train takes 9 hours more than Rajdhani train, so:
(816/2x) = (816/x) + 9
Multiplying both sides by 2x, we get:
816 = 2(816) + 9x
9x = 816 - 2(816) = -816
x = -816/9 = -90.67
This is not a possible speed, so we can conclude that our assumption that Rajdhani train is slower than Express train is incorrect.
Now, according to the second condition, when the speed of Express train is doubled, it takes 4 hours less than Rajdhani train, so:
816/x - 4 = 816/(2x)
Multiplying both sides by 2x, we get:
1632 - 4x = 816
4x = 816 - 1632 = -816
x = -816/4 = -204
Again, this is not a possible speed, so we need to flip our assumption and assume that Rajdhani train is actually faster than Express train.
Let the speed of Rajdhani train be y km/hr (where y is greater than 0).
Then, the speed of Express train is 2y km/hr.
Now, we can use the same equations as before:
(816/2y) = (816/y) + 9
Multiplying both sides by 2y, we get:
816 = 2(816) + 18y
18y = 816 - 2(816) = -816
y = -816/18 = -45.33
Again, this is not a possible speed, so we can conclude that our assumption that Rajdhani train is faster than Express train is also incorrect.
Therefore, there is no valid solution to this problem.
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To travel 816 km, an Express train takes 9 hours more than Rajdhani train. If however, the speed of the Express train is doubled, it takes 4 hours less than Rajdhani train. What is the speed of Rajdhani train?a)48 km/hrb)62.8 km/hrc)33.2 km/hrd)77.5 km/hrCorrect answer is option 'A'. Can you explain this answer?
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