Q.1. Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 P.M. Train B traveling at 90 km/hr also leaves Mumbai for Delhi at 9 P.M. Train C leaves Delhi for Mumbai at 9 P.M. If all three trains meet at the same time between Mumbai and Delhi, what is the speed of Train C if the distance between Delhi and Mumbai is 1260 kms?
(1) 60 km/hr (2) 90 km/hr (3) 120 km/hr (4) 135 km/hr
Correct Answer - (3)
Solution:
All three trains meet at the same time between Delhi and Mumbai. Which means Train A and Train B are at the same point at that time. This will happen when Train B is overtaking Train A.
Train A starts 3 hours before Train B. Therefore, by the time Train B leaves Mumbai, Train A has covered 3 * 60 = 180 kms.
The relative speed between Train A and Train B = 90 - 60 = 30 kmph. Therefore, Train B will overtake Train A in = 6 hours from the time Train B leaves Mumbai. That is at 3 A.M, Train B will overtake Train A. The point between Mumbai and Delhi at which Train B overtakes Train A will be 6*90=540 kms from Mumbai.
Train C will also be at that point at 3 A.M while Train B is overtaking Train A. And Train C would have travelled 1260-540 = 720 kms in these 6 hours. Therefore, the speed of Train C = 120 km/hr.
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Q.2 A train travels at an average speed of 90 km/hr without any stoppages. However, its average speed decrease to 60km/hr on account of stoppages. On an average, how many minutes per hour does the train stop?
(1) 12 minutes (2) 18 minutes (3) 24 minutes (4) 20 minutes
Correct Answer - (4)
Solution:
If it travelled at 90 km / hr, it would have crossed 90 kms in an hour. However, it covered only 60 kms due to stoppages.
The distance it covered decreased by 1/3 or it covered only 2/3rd of the distance that it can cover for which the traveling time would have been 2/3rd of an hour. The remaining 1/3rd of an hour was spent in stoppages. Therefore, the train stops on an average for 20 minutes every hour.
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Q.3 A man goes from city A to city B situated 60 kms apart by a boat. His onward journey was with the stream while the return journey was an upstream journey. It took him four and half hours to complete the round trip. If the speed of the stream is 10 km/hr, how long did it take him to complete the onward journey?
(1) 3 hours (2) 3.5 hours (3) 2.25 hours (4) 1.5 hours
Correct Answer - (4)
Solution:
The average speed for the round trip = km/hr
Let the speed during the onward journey be ‘D’ km/hr. Let the speed of the boat in still water be ‘B’ km/hr.
Therefore, D = B + S => D = B + 10 (As the speed of the stream is 10 km/hr).
Let the speed during the return journey be ‘U’ km/hr.
Therefore, U = B - S = B - 10
As the distance between A and B is the same as the distance between B and A, the average speed is given by the formula =
=> => 3B2 - 300 = 80B.
=> 3B2 - 80B - 300 = 0 => 3B2 - 90B + 10B - 300 = 0
=> 3B(B - 30)+10(B - 30) = 0
=> (B-30)(3B+10) = 0
=> B = 30 or B = -10/3
As speed is a positive quantity, B = 30.
Therefore, D = 30 + 10 = 40 km/hr and U = 30 - 10 = 20 km/hr.
His onward journey was done at a speed of 40 km/hr. The distance covered was 60 kms.
Therefore, the time taken for the onward journey = 1.5 hours
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Q. 4 The speed of a motor boat itself is 20 km/h and the rate of flow of the river is 4 km/h. Moving with the stream the boat went 120 km. What distance will the boat cover during the same time going against the stream?
(1) 80 km (2) 180 km (3) 60 km (4) 100 km
Correct Answer - (1)
Solution:
Let the distance to be covered by the boat when it is travelling against the stream be x.
The boat goes down the river at a speed of 20 + 4 = 24 km/h and up the river at a speed of 20 – 4 = 16 km/h.
Since the time taken is same 120/24 = x/16
Therefore, x = 80 km.
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Q. 5 A passenger train covers the distance between stations X and Y, 50 minutes faster than a goods train. Find this distance if the average speed of the passenger train is 60 kmph and that of goods train is 20 kmph.
(1) 20 kms (2) 25 kms (3) 45 kms (4) 40 kms
Correct Answer - (2)
Solution:
Let ‘d’ be the distance between the stations X and Y.
Time taken by the passenger train to cover the distance ‘d’ = d/60 hour
Time taken by the goods train to cover the distance ‘d’ = d/20 hour
Time difference between these two trains is given by 50 minutes or 50/60 hour
i.e., d/20 –d/60 = 50/60
d = 25kms.
Solve this exercise & check your answers with those given at the end.
1. 2 hours after a freight train leaves Delhi a passenger train leaves the same station travelling in the same direction at an average speed of 16 km/hr. After travelling 4 hrs the passenger train overtakes the freight train. The average speed of the freight train was?
A. 30
B. 40
C.58
D. 60
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2. If a boat is moving in upstream with velocity of 14 km/hr and goes downstream with a velocity of 40 km/hr, then what is the speed of the stream ?
(a) 13 km/hr
(b) 26 km/hr
(c) 34 km/hr
(d) none of these
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3. Two trains move in the same direction at 50 kmph and 32 kmph respectively. A man in the slower train
observes the 15 seconds elapse before the faster train completely passes by him.
What is the length of faster train ?
(a) 100m
(b) 75m
(c) 120m
(d) 50m
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4. I drove 60 km at 30 kmph and then an additional 60 km at 50 kmph. Compute my average speed over my 120 km.
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5. If a car starts from A towards B with some velocity due to some problem in the engine after travelling 30km.If the car goes with 4/5 th of its actuval velocity the car reaches B 45min later to the actual time. If the car engine fails ofter travelling 45km, the car reaches the destination B 36min late to the actual time , what is the initial velocity of car and what is the distance between A and B in km
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6. Two trains are travelline at equilateral .Train A is travelling in the direction of earths spin.Other train B is travelling in opposite direction of earths spin.Which trains wheels will wear first?and why?
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7. A person, who decided to go to weekend trip should not exceed 8 hours driving in a day. Average speed of forward journey is 40 m/h. Due to traffic in Sundays, the return journey average speed is 30 m/h. How far he can select a picnic spot?
a) 120 miles
b) Between 120 and 140 miles
c) 160 miles
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8. A person was fined for exceeding the speed limit by 10mph. Another person was also fined for exceeding the same speed limit by twice the same. If the
second person was traveling at a speed of 35 mph, find the speed limit.
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9. A bus started from bus stand at 8.00am, and after 30 minutes staying at
destination, it returned back to the bus stand. The destination is 27 miles from
the bus stand. The speed of the bus is 18mph. In return journey bus travels
with 50% fast speed. At what time it returns to the bus stand?
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10. A train goes from a to b. If it travels with 50 km/s then it is late by 10 mins. When it travels with30km/s then it is late by 50 mins. Find the distance between a and b.
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ANSWERS
Ans 1. B
Ans 2. A
Ans 3: B
Ans 4: 37 1/2
Explanation : Time reqd for the first 60 km = 120 min.; Time reqd for the second 60 km = 72 min.; Total time reqd = 192 min
Avg speed = (60*120)/192 = 37 1/2
Ans 5. 20 & 130.
Ans 6:TRAIN B .Because of less centrifugal force.
Ans 7: 120 miles
Ans 8: Let ‘x’ be the speed limit
Person ‘A’ was fined for exceeding the speed limit by = 10mph
Person ‘B’ was fined for exceeding the speed limit by = twice of ‘A’
= 2*10mph=20mph
given that the second person was traveling at the speed of 35mph
=> 35mph – 20mph = 15mph
Therefore the speed limit is =15 mph
Ans 9: 11.00am
