Question 1 1 / -0
A thief steals a car at 1:30 p.m. and drives at 40 kmph. At 2:00 p.m, the owner of the car starts chasing his car at 50 kmph. At what time will he catch the thief?
Solution
Distance covered by the thief in 1 hour = 40 km
Distance covered in
hour = 20 km
Now, time taken to catch the thief =
Relative velocity = 50 kmph - 40 kmph = 10 kmph (
both are moving in the same direction)
Time taken to catch the thief =
hours = 2 hours
Time = 4:00 p.m. (
2:00 p.m. + 2 hours)
Question 2 1 / -0
Sonu rides at a rate of 10 km per hour, but stops for 10 minutes to take rest at the end of every 15 km. How many hours will she take to cover 100 km?
Solution
In a total of 100 km, number of stoppages after every 15 km is 6 (15
6 = 90)
Now, time taken for 100 km journey =
= 10 hours
Total time for stoppages = 6
10 min = 60 min or 1 hour
She will take total (10 + 1) = 11 hours to complete the journey.
Question 3 1 / -0
On a river, B is an intermediate station equidistant from stations A and C. A boat can go from A to B and come back in 6 hours. If it takes 4 hours to go from A to C, then how long would it take to go from C to A?
Solution
Time taken from A to C = 4 hours
Time taken from A to B = 2 hours (Since B is intermediate)
Also time taken from A to B and B to A = 6 hours
Time taken from B to A = 6 - 2 = 4 hours
Hence, Time taken from C to A = 2 × 4 = 8 hours.
Question 4 1 / -0
A train is travelling at a speed of 48 km/h. A passenger counts the telegraph posts on the way as the train passes them. If the posts are 50 metres apart, then how many posts will he cross per minute?
Solution
Speed of the train = 48 km/h =
m/min = 800 m/min
Number of telegraph posts = 800/50 = 16
Question 5 1 / -0
Excluding stoppages, the average speed of a bus is 45 kmph and including stoppages, its average speed is 36 kmph. For how many minutes does the bus stop per hour?
Solution
Bus will travel 45 km without stoppages and 36 km with stoppages in one hour.
Difference of 9 km's time is wasted in stoppages.
∴ Time wasted in stoppages per hour =
=
hours = 12 minutes
Question 6 1 / -0
The wheel of an engine 25 decimetre in circumference makes 16 revolutions in 4 seconds. The speed of the wheel (in kmph) is
Solution
Distance covered in 1 revolution = 25 dm
Distance covered in 16 revolutions = 25 × 16 = 400 dm
Time taken to complete 400 dm = 4 sec
In m/s =
= 10 m/s {dm = 0.1m}
Speed of wheel = 10
kmph = 36 kmph
Question 7 1 / -0
A man covered a certain distance by train at the rate of 25 kmph and walked back at the rate of 4 kmph. The whole journey took 5 hour 48 minutes. What distance did he ride?
Solution
Let the total distance be x km.
Then,
x = 20 km
Question 8 1 / -0
Two trains, having lengths 210 metres and 270 metres, are moving in the same direction with speeds of 46 km/hr and 54 km/hr, respectively. How long will the trains take to pass each other?
Question 9 1 / -0
A and B run a 2 km race. A gives B a start of 100 m and still beats him by 20 seconds. If A runs at 20 kmph, find B's rate in kmph.
Solution
A covers the distance of 2 km in (2/20) hours, i.e. 360 seconds.
B covers the distance of (2000 – 100), i.e. 1900 m in 360 + 20, i.e. 380 seconds.
B's speed = (1900/380) = 5 m/s = 5
= 18 kmph
Question 10 1 / -0
Two trains start at the same time from station A and station B and proceed towards each other at the rate of 16 km per hour and 21 km per hour, respectively. When they meet, it is found that one train has travelled 60 km more than the other. The distance between the two stations is
Solution
Distance between the two stations =
= 60
= 60
= 444 km
Question 11 1 / -0
Two persons start from A and B with the speed of 25 kmph and 49 kmph, respectively towards each other. After they cross each other, the person from B covers 145 km to reach A. What is the distance (in km) between A and B?
Solution
Let the two meet after a time of t hours.
Distance covered by A in t hours = 25 t km
So, 25 t = 145
Or, t =
Distance covered by B in this time = 49 t km = 284.2 km
Thus, total distance between A and B = 284.2 km + 145 km = 429.2 km
Question 12 1 / -0
A ship went on a voyage. After it had travelled 180 miles, a plane started from the same starting point, as of the ship, with 10 times the speed of the ship. How far from the starting point would they be when they are at the same distance(in miles) from the starting point?
Solution
Let speed of the ship = x mph
Question 13 1 / -0
A ball moves at 120 metres per second and strikes an object in three seconds. If it moves at 100 metres per second, how long does it take to strike the same object?
Solution
Total distance covered by ball = 120
3 m = 360 m
Now, speed of ball = 100 m/s
Time taken =
s =
s
Question 14 1 / -0
Tony starts for his office at a speed of 40 kmph. If he travels at this speed, he will reach his office exactly on time. But after travelling 20 km, he realises that he has forgotten an important document back at home. So, he goes back home at a speed of 60 kmph, collects the document and again starts for his office at a speed of 80 kmph and reaches his office exactly on time. What is the distance between his home and his office?
Solution
If the distance between home and office is `d` km, then he needs
hr to reach his office.
So,
=
+
+
d =
= 66
km
Question 15 1 / -0
Brown starts 2 hours after John and overtakes him in 4 hours. If the difference between the speeds of John and Brown is 20 kmph, what is the distance travelled by Brown before meeting John?
Solution
Let John's speed be x kmph.
Question 16 1 / -0
A train of length 120 metres overtakes another train of length 100 metres in 8 seconds. If the speed of the slower train is 27 kmph, what is the speed of the faster train?
Solution
Length of the first train = 120 m
Length of the second train = 100 m
Distance = 220 m
time (t) = 8 sec --- (1)
Speed of slower train(v
1 ) = 27 kmph = 27 ×
m/s = 7.5 m/s
Speed of the faster train = v
2 Relative speed = v
2 - v
1 -- (2)
From (1) and (2),
v
2 - v
1 =
= 27.5 m/s
v
2 = 35 m/s = 35 ×
kmph = 126 kmph
Question 17 1 / -0
A boat takes 6 hours to travel from A to B (upstream). The river flows at the rate of 2 kmph. How long will the boat take to travel from B to A (downstream), if the distance from A to B is 36 km?
Solution
Upstream:
Let t be the time taken by the boat to travel from A to B = 6 hours
Let V
1 be the speed of the boat travelling upstream = x
Let V
2 be the speed of the stream = 2 kmph
Distance = 36 km
V
1 - V
2 =
= 6 kmph
V
1 = 8 kmph
Downstream:
V
1 = 8 kmph
V
2 = 2 kmph
Net speed = V
1 + V
2 = 10 kmph
Distance = 36 km
Time =
= 3.6 hours
Question 18 1 / -0
A train crosses a platform in 60 seconds, travelling at a speed of 54 kmph. If the length of the platform is 500 metres, what is the length of the train?
Solution
Time = t = 60 s
Speed of train = 54 kmph = 15 m/s
Length of platform = l
1 = 500
Length of train = l
2 Then, according to the question:
15 =
=
l
2 = 900 - 500 = 400 m
Question 19 1 / -0
A man reaches his office 5 minutes late when he travels at the speed of 8 kmph. However, when he increases his speed to 12 kmph, he reaches 5 minutes early. What is the distance that he travels?
Solution
Let the normal time taken to reach the office be t hours.
Distance = d km = 8(t +
) km = 12(t -
) km
Solving this, we get:
t =
d = 8
= 4
Thus, the distance is 4 km.
Hence, answer option 1 is correct.
Question 20 1 / -0
A man rows down a river 15 km in 3 hours with the stream and returns in 7
hours. The rate at which he rows in still water is
Solution
Speed of the row downstream =
= 5 km/hr
Speed of the row upstream =
= 2 km/hr
Speed of the row in still water =
= 3.5 km/hr
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