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Two, trains, one from Mumbai to New Delhi and the other from New Delhi to Mumbai, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. What is the ratio of their speed?
- a)5:4
- b)4:3
- c)3:2
- d)2:1
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two, trains, one from Mumbai to New Delhi and the other from New Delh...
Standard Formula: If two objects A and B begin their journey at the same time from two points P and Q towards each other and after crossing each other they take a and b hours in reaching Q and P respectively, then
A's Speed Vb
B's Speed Va
By looking at the above problem, we can say that, a=9 hours, b=16 hours.
Therefore, Ratio of speeds of two trains = V16/V9 = 4/3 or 4:3
Most Upvoted Answer
Two, trains, one from Mumbai to New Delhi and the other from New Delh...
Solution:
Let the distance between Mumbai and New Delhi be d km.
Let the speed of the Mumbai to New Delhi train be x km/hr.
Let the speed of the New Delhi to Mumbai train be y km/hr.
When the two trains meet, their total distance travelled is equal to the distance between Mumbai and New Delhi, i.e. d km.
Time taken by Mumbai to New Delhi train to cover the distance = 9 hours
Time taken by New Delhi to Mumbai train to cover the distance = 16 hours
Formula: Distance = Speed × Time
Distance travelled by Mumbai to New Delhi train = x × 9 = 9x km
Distance travelled by New Delhi to Mumbai train = y × 16 = 16y km
Total distance travelled = 9x + 16y
9x + 16y = d ...........(1)
We can also calculate the time taken by both trains to meet each other.
Formula: Time = Distance / Speed
Time taken by Mumbai to New Delhi train to meet New Delhi to Mumbai train = d / (x + y)
As both the trains start simultaneously, the time taken by both trains to meet each other will be the same.
So, d / (x + y) = 9 = 16
d / (x + y) = 144 ...........(2)
From equation (1), we get
9x + 16y = d
x + y = d / 25 ...........(3)
Substituting equation (3) in equation (2), we get
d / (d / 25) = 144
25 × 144 = d
d = 3600 km
Substituting d = 3600 km in equation (1), we get
9x + 16y = 3600
x + y = 3600 / 25
x + y = 144
Solving these equations, we get
x = 64 km/hr
y = 80 km/hr
Ratio of their speed = x : y
= 64 : 80
= 4 : 5
Hence, the answer is option (b) 4 : 3.
Let the distance between Mumbai and New Delhi be d km.
Let the speed of the Mumbai to New Delhi train be x km/hr.
Let the speed of the New Delhi to Mumbai train be y km/hr.
When the two trains meet, their total distance travelled is equal to the distance between Mumbai and New Delhi, i.e. d km.
Time taken by Mumbai to New Delhi train to cover the distance = 9 hours
Time taken by New Delhi to Mumbai train to cover the distance = 16 hours
Formula: Distance = Speed × Time
Distance travelled by Mumbai to New Delhi train = x × 9 = 9x km
Distance travelled by New Delhi to Mumbai train = y × 16 = 16y km
Total distance travelled = 9x + 16y
9x + 16y = d ...........(1)
We can also calculate the time taken by both trains to meet each other.
Formula: Time = Distance / Speed
Time taken by Mumbai to New Delhi train to meet New Delhi to Mumbai train = d / (x + y)
As both the trains start simultaneously, the time taken by both trains to meet each other will be the same.
So, d / (x + y) = 9 = 16
d / (x + y) = 144 ...........(2)
From equation (1), we get
9x + 16y = d
x + y = d / 25 ...........(3)
Substituting equation (3) in equation (2), we get
d / (d / 25) = 144
25 × 144 = d
d = 3600 km
Substituting d = 3600 km in equation (1), we get
9x + 16y = 3600
x + y = 3600 / 25
x + y = 144
Solving these equations, we get
x = 64 km/hr
y = 80 km/hr
Ratio of their speed = x : y
= 64 : 80
= 4 : 5
Hence, the answer is option (b) 4 : 3.
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Two, trains, one from Mumbai to New Delhi and the other from New Delhi to Mumbai, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. What is the ratio of their speed?a) 5:4b) 4:3c) 3:2d) 2:1Correct answer is option 'B'. Can you explain this answer?
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