Speed, Time and Distance
- The ratio between the rates of travelling of A and B is 2:3 and therefore A takes 10 min. more than the time taken by B to reach a destination, if A had walked at double the speed, he would have covered the distance in ?
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Ratio of times taken by A and B = 1/2 : 1/3
Suppose B takes Tb min. Then A takes (Tb + 10) min.
∴ (Tb + 10 ) : Tb = 1/2: 1/3
⇒ (Tb + 10)/Tb = 3 / 2
⇒ 2Tb + 20 = 3Tb
∴ Tb = 20
Correct Option: C
Ratio of times taken by A and B = 1/2 : 1/3
Suppose B takes Tb min. Then A takes (Tb + 10) min.
∴ (Tb + 10 ) : Tb = 1/2: 1/3
⇒ (Tb + 10)/Tb = 3 / 2
⇒ 2Tb + 20 = 3Tb
∴ Tb = 20
∴ Time taken by A = 20 +10
= 30 minute
If A had walked at double speed
Req . time = 30/2
=15 minute
- A man travel 35 km partly at 4 km/hr if he covers former distance at 5 km/hr and later distance at 4 km/hr he could cover 2 km. more in the same time. The time taken to cover the whole distance at original rate is ?
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Suppose the man covers first distance in x hrs and second distance in y hrs.
Then, 4x + 5y = 35 and 5x + 4y = 37Correct Option: D
Suppose the man covers first distance in x hrs and second distance in y hrs.
Then, 4x + 5y = 35 and 5x + 4y = 37
Solving these equations, we get
x = 5 and y = 3
∴ Total time taken = 5 + 3 hrs.
= 8 hrs.
- If a train run at 40 km/hr it reaches its destination late by 11 min but if it run at 50 km/hr it is late by 5 min only. The correct time for the train to cover at journey is ?
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Let the required time = T min.
Then, distance covered in T + 11 min at 40 km/hr = distance covered in T + 5 min at 50 km/hr.
⇒ 40 ( T + 11 ) / 60 = 50 (T + 5 ) / 60Correct Option: D
Let the required time = T min.
Then, distance covered in T + 11 min at 40 km/hr = distance covered in T + 5 min at 50 km/hr.
⇒ 40 ( T + 11 ) / 60 = 50 (T + 5 ) / 60
∴ T = 19 min.
- A train Meerut at 6 a.m. and reaches Delhi at 10 a.m. another train leaves Delhi at 8 a.m. and reaches Meerut at 11:30 a.m. at what time do trains cross one another ?
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Let the distance between Meerut and Delhi be y km.
Average speed of the train leaving Meerut = y/4 km/hr.
Average speed of the train leaving Delhi = 2y/7 km/hr.
suppose they meet x hrs. after 6 a.m
then, xy/4 + 2y (x-2)/7 = y
⇒ x/4 + 2x-4/7 = 1
⇒ 15x = 44
Correct Option: D
Let the distance between Meerut and Delhi be y km.
Average speed of the train leaving Meerut = y/4 km/hr.
Average speed of the train leaving Delhi = 2y/7 km/hr.
suppose they meet x hrs. after 6 a.m
then, xy/4 + 2y (x-2)/7 = y
⇒ x/4 + 2x-4/7 = 1
⇒ 15x = 44
∴ x = 44/15 = 2 hrs. 56 min
So, the train meet at 8:56 a.m
- A train leaves Delhi at 5 a.m. and reaches Kanpur at 10 a.m. another train leaves Kanpur at 7 a.m. and reaches Delhi at 2 p.m. at what time do the two trains meet ?
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Let the distance between Delhi and Kanpur be y km .
Suppose the train leaving from Delhi is A and the train leaving from Kanpur B
A's speed = y/ (10 a.m - 5 a.m) = y/5 km/hr.
B's Speed = y/ (2 p.m - 7 a.m) = y/7 km/hr.
Since B starts two hours later than A, the distance already covered by A at the start of B = 2y/5 km.
Remaining distance = y- 2y/5 = 3y/5 km.
Relative speed of approach of two trains = (y/5 + y/7)
= 12y/35 km/hr.Correct Option: A
Let the distance between Delhi and Kanpur be y km .
Suppose the train leaving from Delhi is A and the train leaving from Kanpur B
A's speed = y/ (10 a.m - 5 a.m) = y/5 km/hr.
B's Speed = y/ (2 p.m - 7 a.m) = y/7 km/hr.
Since B starts two hours later than A, the distance already covered by A at the start of B = 2y/5 km.
Remaining distance = y- 2y/5 = 3y/5 km.
Relative speed of approach of two trains = (y/5 + y/7)
= 12y/35 km/hr.
Time taken to cover the remaining distance by both trains = (3y / 5) / (12y / 35)
= (3/5) x (35/12) = 7/4 hrs.
= 1 hr. 45 min.
∴ The two train will meet at (7 a.m + 1hr.45 min)
= 8.45 a.m
