1. A man traveled from the village to the post office at the rate of
25 km/h and walked back at the rate of 4 km/h. If the whole journey took
5 hours 48 min. Find the distance of the post -office from the village .
(a) 40 km (b) 80 km
(c) 10 km (d) 20 km
Answer: (d) 20 km
Solution:
Using the formula mentioned in the shortcut formulas for speed, time and distance:
We have,
Average for the whole distance = (2x25x4)/(25 + 4) = (200/29) km/hr
It is given that the total time taken =
5 hours48 minutes = 5+48/60 = 5 + 4/5 = 29/5 hrs
Therefore, total distance to and fro, from the village to the post-office =
(200/29)(29/5) = 40 km
Thus, the distance from the village to the post office = 40/2 = 20 km
2. A car travels a distance of 170 km in 2 hours, partly at a speed of 100 km/hr and partly at 50 km/hr. Find the distance traveled at a speed of 100 km/hr.
(a) 160 km (b) 120 km
(c) 140 km (d) 220 km
Answer:(c) 140 km
Solution:
Let the distance traveled at 100 km/hr be x km.
Then the distance traveled at 50 km/hr is (170 - x )
Therefore, according to the conditions given in the question, we have
(x/100) + [(170-x)/50)] = 2
=> x/100 + 170/50 - x/50 = 2
=> x/100 - x/50 = 2 - 170/50
=> (x - 2x)/100 = (100-170)/50
=> (-x)/100 = -70/50
=> x = (70/50)(100)
= 140 km
Thus, 140 km is the distance traveled at 100 km/hr.
3. The ratio between the speed of Ram and Shyam is 6:7 . If Ram takes 30 minutes more than Shyam to cover a distance. Then find the actual time taken by Ram and Shyam ?
(a) 7/2,3 hrs (b) 3/5,8 hrs
(c) 5/2,9 hrs (d) 4/1,2 hrs
Answer: (a) 7/2,3 hrs
Solution:
Let the speed of Ram and Shyam be 6x km/hr and 7x km/hr and the distance be D km.
Then, according to the conditions given in the question, we have
D/6x - D/7x = 1/2
=> (7D - 6D)/42x =1/2
=> D/42 x = 1/2
=> D = 21x km
Now, Speed of Ram = (21x)/6x =7/2 hours
and speed of Shyam = (21x)/7x = 3 hours
4. A road is of 900 km length. A contractor wants to plant some pillars on the road at 10 km of distance. Find the total no of pillars that the controller has to plant.
(a) 67 (b) 136
(c) 91 (d) 22
Answer:(c) 91
Solution:Total length of the road = 900 km.
A pillar is planted after every 10 km, therefore total pillar to be planted
= 900km/10km + 1
= 90 + 1
= 91
Note:1 is added to the division of (900/10) because the first pillar was posted at 0 km.
5. A monkey tries to ascend a greased pole 14 meters high. He ascends 2 meters in first minutes and slips down 1 meter in the alternate minute. If he continues to ascend in this fashion, how long does he take to reach the top ?
(a) 14 minute (b) 24 minute
(c) 25 minute (d) 28 minutes
Answer: (c) 25 minute
Solution:
Money ascends 2 meters in 1 minute and slips 1 meter in the next minute.
So, In 2 minute, he ascend 1 meter.
to reach 12 meter, he needs 12 x 2 = 24 minutes.
Again, in the 25th minutes he ascends to 14 meter and therefore at the end of 25th minute he reaches the top.
6. Krishna covers a certain distance by train at 25 km/hr and the same distance on foot at 4 km/hr. If the time taken by him for the whole journey by 5 hrs and 48 minutes. How much total did her cover ?
(a) 42 km (b) 40 km
(c) 69 km (d) 98 km (e) None of the
Answer: (b) 40 km
Solution: see question number 1 above, you will see that the total distance traveled will come out be 40 km.
7. If a 100 meters long train which is moving at 50 km per hour crosses another train which is 120 meter long and moving in opposite direction in 6 seconds. What is the speed of the second train ?
(a) 40 km/hr (b) 82 km/hr
(c) 120 km/hr (d) 60 km/hr
Answer: (b) 82 km/hr
Solution:
Let the speed of the second train be x km/hr.
If two trains are traveling opposite to each other (on different tracks obviously) then the relative speed of the trains would be the sum of the speeds of the two trains.
for more formula related to trains
read: shortcuts formulas time, speed and distance
Therefore,
Relative speed = (50 km/hr + x km/hr) = (50 + x) km/hr. = (50 +x)(5/18) m/s
Again,
total distance traveled by the trains = (100 + 120)m=220m in 6 seconds.
Therefore, according to the conditions given in the question, we have
220 /{(50 + x)(5/18)} = 6
=> 220 = 6{(50 + x)(5/18)}
=> 220/(5/18) = 300 + 6x
=> (220 x 18)/5 = 300 + 6x
=> (44 x 18 ) = 300 + 6x
=> 792 - 300 = 6x
=> 492/6 = x
=> x = 82
Therefore, the speed of the second train = 82 km/hr.
8. Two horse riders are at two different places 30 km apart. They rode towards one another.If their speeds are 15 km/hr and 12 km/hr respectively. After what time will they meet together ?
(a) 2 hour 40 min (b) 1 hour 45 min
(c) 1 hour 40 min (d) 1 hour 6 min 40 sec
Answer: (d) 1 hour 6 min 40 sec
Solution:
Since,they are riding towards each other, their relative speed=(15 + 12)=27km/hr
Again, they are 30 km apart, time taken to cover this distance
= (30)/27 hours
= 10/9 km = (1 + 1/9) hour
= 1 hour + 60/9 minutes
= 1 hour + 20/3 minutes
= 1 hour + 6 minutes + 2/3 minute
= 1 hour 6 minutes 40 sec
9. If a train running at the speed of 30 m/sec crosses a 600 meters long platform in 30 seconds. What is the length of the train ?
(a)120 m (b) 200 m
(c) 300 m (d) 150 m
Answer:(c) 300 m
Solution:
Let the length of the train be x meter.
For such question, total length traveled by the train is the sum of the length of the train and the length of the platform.
Therefore, according to the conditions given in the question
=> (600 + x)/30 = 30
=> 600 + x = 900
=> x = 300 m
10. If a wheel of train takes 4 round in a second and the diameter of the wheel is 84 cm. What is its speed in kilometers per hour ? (here π = 22/7)
(a) 38.016 (b) 38.00
(c) 31.16 (d) 39
Answer:(a) 38.016
Solution: Circumference of the wheel is (π)(d) = (22/7)(0.84) =2.64 m
It is given that the wheel makes 4 turns per second. In 1 second the wheel covers
2.64 m x 4 = 10.56 m/s
And 10.56m/s = (10.56)(18/5) = 38.016 km/hr
11. In how many second a cyclist will pass a distance of 100 meters at the speed of 10 km per hours ?
(a) 25 (b) 36
(c) 40 (d) 42
Answer: (b) 36
Solution:
Speed of cyclist = 10 km/hr = (10)(5/18) m/s = (25/9) m/s
Time taken to pass 100 m = (100)/(25/9) = (100 x 9)/25 = 36 seconds
12. A train crosses a platform 100 meter long in 15 seconds and a man standing on a platform in 10 seconds. What is speed of the train ?
(a) 38 km/hr (b) 72 km/hr
(c) 75 km/hr (d) 70 km/hr
Answer: (b) 72 km/hr
Solution:
Let the length of the train be x m and the speed be s m/sec.
Then, According to the conditions of the question, we have
(100 + x )/ s = 15 ---------------(i)
And (x)/s = 10 ---------------(ii)
from (i) 100/s + x/s = 15
=> 100/s + 10 = 15 ( from (ii))
=> 100/s = 5
=> s = 100/5
=> s = 20 m/s
Thus, in km/hr the speed of the train = (20)(18/5) = 72 km/hr
13. If a train is running at the speed of 864 km/hr. How much distance will it cover in 10 minutes ?
(a) 0.014 km (b) 144 km
(c) 14.4 km (d) 1.44 km
Answer: (b) 144 km
Solution:
Distance covered in 10 min or 1/6 hours = (1/6)(864) = 144 km
14. A man walks a certain distance at 8 km/hr and returns at 6 km/hr. If the total time taken by him is 3 and 1/2 hours, the total distance walked is?
(a) 28 km (b) 24 km
(c) 14 km (d) 16 km
Answer: (b) 24 km
Solution:
Average speed of the entire journey = (2x8x6)/(8 + 6) = (96)/(14)=48/7 km/hr
And total time taken = (48/7)(7/2) = 24 km
15. A man is walking at a speed of 12 km per hour. After every km he takes rest for 12 minutes. How much time will he take to cover a distance of 36 km ?
(a) 30 hours (b) 10 hours
(c) 25 hours (d) 40 hours
Answer: (b) 10 hours
Solution:
For a distance of 36 km , he will stop for rest for 35 times. ( 36 -1 because after the end of 36 km he would have reached the destination)
Therefore, total time he rested = 35 x 12 = 420 min = 7 hours
And had he not rested, time taken would have been = (36)/12 = 3 hours
Therefore, total time taken = 7 + 3 = 10 hours
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For more questions on time, speed and distance : read- questions on Time, speed and distance
For questions on time and work : read - questions on time and work
(a) 40 km (b) 80 km
(c) 10 km (d) 20 km
Answer: (d) 20 km
Solution:
Using the formula mentioned in the shortcut formulas for speed, time and distance:
We have,
Average for the whole distance = (2x25x4)/(25 + 4) = (200/29) km/hr
It is given that the total time taken =
5 hours48 minutes = 5+48/60 = 5 + 4/5 = 29/5 hrs
Therefore, total distance to and fro, from the village to the post-office =
(200/29)(29/5) = 40 km
Thus, the distance from the village to the post office = 40/2 = 20 km
2. A car travels a distance of 170 km in 2 hours, partly at a speed of 100 km/hr and partly at 50 km/hr. Find the distance traveled at a speed of 100 km/hr.
(a) 160 km (b) 120 km
(c) 140 km (d) 220 km
Answer:(c) 140 km
Solution:
Let the distance traveled at 100 km/hr be x km.
Then the distance traveled at 50 km/hr is (170 - x )
Therefore, according to the conditions given in the question, we have
(x/100) + [(170-x)/50)] = 2
=> x/100 + 170/50 - x/50 = 2
=> x/100 - x/50 = 2 - 170/50
=> (x - 2x)/100 = (100-170)/50
=> (-x)/100 = -70/50
=> x = (70/50)(100)
= 140 km
Thus, 140 km is the distance traveled at 100 km/hr.
3. The ratio between the speed of Ram and Shyam is 6:7 . If Ram takes 30 minutes more than Shyam to cover a distance. Then find the actual time taken by Ram and Shyam ?
(a) 7/2,3 hrs (b) 3/5,8 hrs
(c) 5/2,9 hrs (d) 4/1,2 hrs
Answer: (a) 7/2,3 hrs
Solution:
Let the speed of Ram and Shyam be 6x km/hr and 7x km/hr and the distance be D km.
Then, according to the conditions given in the question, we have
D/6x - D/7x = 1/2
=> (7D - 6D)/42x =1/2
=> D/42 x = 1/2
=> D = 21x km
Now, Speed of Ram = (21x)/6x =7/2 hours
and speed of Shyam = (21x)/7x = 3 hours
4. A road is of 900 km length. A contractor wants to plant some pillars on the road at 10 km of distance. Find the total no of pillars that the controller has to plant.
(a) 67 (b) 136
(c) 91 (d) 22
Answer:(c) 91
Solution:Total length of the road = 900 km.
A pillar is planted after every 10 km, therefore total pillar to be planted
= 900km/10km + 1
= 90 + 1
= 91
Note:1 is added to the division of (900/10) because the first pillar was posted at 0 km.
5. A monkey tries to ascend a greased pole 14 meters high. He ascends 2 meters in first minutes and slips down 1 meter in the alternate minute. If he continues to ascend in this fashion, how long does he take to reach the top ?
(a) 14 minute (b) 24 minute
(c) 25 minute (d) 28 minutes
Answer: (c) 25 minute
Solution:
Money ascends 2 meters in 1 minute and slips 1 meter in the next minute.
So, In 2 minute, he ascend 1 meter.
to reach 12 meter, he needs 12 x 2 = 24 minutes.
Again, in the 25th minutes he ascends to 14 meter and therefore at the end of 25th minute he reaches the top.
6. Krishna covers a certain distance by train at 25 km/hr and the same distance on foot at 4 km/hr. If the time taken by him for the whole journey by 5 hrs and 48 minutes. How much total did her cover ?
(a) 42 km (b) 40 km
(c) 69 km (d) 98 km (e) None of the
Answer: (b) 40 km
Solution: see question number 1 above, you will see that the total distance traveled will come out be 40 km.
7. If a 100 meters long train which is moving at 50 km per hour crosses another train which is 120 meter long and moving in opposite direction in 6 seconds. What is the speed of the second train ?
(a) 40 km/hr (b) 82 km/hr
(c) 120 km/hr (d) 60 km/hr
Answer: (b) 82 km/hr
Solution:
Let the speed of the second train be x km/hr.
If two trains are traveling opposite to each other (on different tracks obviously) then the relative speed of the trains would be the sum of the speeds of the two trains.
for more formula related to trains
read: shortcuts formulas time, speed and distance
Therefore,
Relative speed = (50 km/hr + x km/hr) = (50 + x) km/hr. = (50 +x)(5/18) m/s
Again,
total distance traveled by the trains = (100 + 120)m=220m in 6 seconds.
Therefore, according to the conditions given in the question, we have
220 /{(50 + x)(5/18)} = 6
=> 220 = 6{(50 + x)(5/18)}
=> 220/(5/18) = 300 + 6x
=> (220 x 18)/5 = 300 + 6x
=> (44 x 18 ) = 300 + 6x
=> 792 - 300 = 6x
=> 492/6 = x
=> x = 82
Therefore, the speed of the second train = 82 km/hr.
8. Two horse riders are at two different places 30 km apart. They rode towards one another.If their speeds are 15 km/hr and 12 km/hr respectively. After what time will they meet together ?
(a) 2 hour 40 min (b) 1 hour 45 min
(c) 1 hour 40 min (d) 1 hour 6 min 40 sec
Answer: (d) 1 hour 6 min 40 sec
Solution:
Since,they are riding towards each other, their relative speed=(15 + 12)=27km/hr
Again, they are 30 km apart, time taken to cover this distance
= (30)/27 hours
= 10/9 km = (1 + 1/9) hour
= 1 hour + 60/9 minutes
= 1 hour + 20/3 minutes
= 1 hour + 6 minutes + 2/3 minute
= 1 hour 6 minutes 40 sec
9. If a train running at the speed of 30 m/sec crosses a 600 meters long platform in 30 seconds. What is the length of the train ?
(a)120 m (b) 200 m
(c) 300 m (d) 150 m
Answer:(c) 300 m
Solution:
Let the length of the train be x meter.
For such question, total length traveled by the train is the sum of the length of the train and the length of the platform.
Therefore, according to the conditions given in the question
=> (600 + x)/30 = 30
=> 600 + x = 900
=> x = 300 m
10. If a wheel of train takes 4 round in a second and the diameter of the wheel is 84 cm. What is its speed in kilometers per hour ? (here π = 22/7)
(a) 38.016 (b) 38.00
(c) 31.16 (d) 39
Answer:(a) 38.016
Solution: Circumference of the wheel is (π)(d) = (22/7)(0.84) =2.64 m
It is given that the wheel makes 4 turns per second. In 1 second the wheel covers
2.64 m x 4 = 10.56 m/s
And 10.56m/s = (10.56)(18/5) = 38.016 km/hr
11. In how many second a cyclist will pass a distance of 100 meters at the speed of 10 km per hours ?
(a) 25 (b) 36
(c) 40 (d) 42
Answer: (b) 36
Solution:
Speed of cyclist = 10 km/hr = (10)(5/18) m/s = (25/9) m/s
Time taken to pass 100 m = (100)/(25/9) = (100 x 9)/25 = 36 seconds
12. A train crosses a platform 100 meter long in 15 seconds and a man standing on a platform in 10 seconds. What is speed of the train ?
(a) 38 km/hr (b) 72 km/hr
(c) 75 km/hr (d) 70 km/hr
Answer: (b) 72 km/hr
Solution:
Let the length of the train be x m and the speed be s m/sec.
Then, According to the conditions of the question, we have
(100 + x )/ s = 15 ---------------(i)
And (x)/s = 10 ---------------(ii)
from (i) 100/s + x/s = 15
=> 100/s + 10 = 15 ( from (ii))
=> 100/s = 5
=> s = 100/5
=> s = 20 m/s
Thus, in km/hr the speed of the train = (20)(18/5) = 72 km/hr
13. If a train is running at the speed of 864 km/hr. How much distance will it cover in 10 minutes ?
(a) 0.014 km (b) 144 km
(c) 14.4 km (d) 1.44 km
Answer: (b) 144 km
Solution:
Distance covered in 10 min or 1/6 hours = (1/6)(864) = 144 km
14. A man walks a certain distance at 8 km/hr and returns at 6 km/hr. If the total time taken by him is 3 and 1/2 hours, the total distance walked is?
(a) 28 km (b) 24 km
(c) 14 km (d) 16 km
Answer: (b) 24 km
Solution:
Average speed of the entire journey = (2x8x6)/(8 + 6) = (96)/(14)=48/7 km/hr
And total time taken = (48/7)(7/2) = 24 km
15. A man is walking at a speed of 12 km per hour. After every km he takes rest for 12 minutes. How much time will he take to cover a distance of 36 km ?
(a) 30 hours (b) 10 hours
(c) 25 hours (d) 40 hours
Answer: (b) 10 hours
Solution:
For a distance of 36 km , he will stop for rest for 35 times. ( 36 -1 because after the end of 36 km he would have reached the destination)
Therefore, total time he rested = 35 x 12 = 420 min = 7 hours
And had he not rested, time taken would have been = (36)/12 = 3 hours
Therefore, total time taken = 7 + 3 = 10 hours
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For more questions on time, speed and distance : read- questions on Time, speed and distance
For questions on time and work : read - questions on time and work
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