A person rides a bicycle round a circular path of radius 50 m. The radius of the wheel of the bicycle is 50 cm. The cycle comes to the starting point for the first time in 1 hour. What is the number of revolutions of the wheel in 15 minutes?
Circumference of the circular path = 2/\50 = 100 /\ m
This means 100? m is the distance covered in 60 minutes
Therefore distance covered in 15 minutes = 1/4 x 100 /\ m = 25/\ m
Now distance covered in one revolution of the wheel = 2 /\(1/2) m = /\ m
Therefore number of revolutions in 15 minutes = 25/\ //\ = 25
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48
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23
Solv. In. Corr.
71
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2 M:5 S
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2 / 62
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A man reaches his office 30 min late, if he walks from his home at 3 km per hour and reaches 40 min early if he walks 4 km per hour. How far is his office from his house?
Lets assume distance between office and his house =x km
Time taken when speed is 3 kmph = x/3 min.
Time taken when speed is 4 kmph = x/4 min.
Difference between time taken 40-(-30) = 70mins = 70/60 hours.
x/3- x/4 = 70/60
x/12= 7/6
x=14 km
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37
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26
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63
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The distance between 2 persons is 800m. If they start moving towards each other simultaneously at 10m/s and 15m/s, in how much time do they meet?
3/4 of a man's usual speed means, he takes 4/3 of his usual time to cover the same distance,
i.e. he takes 4/3 â€“ 1 = 1/3 time extra.
Given 1/3 time is 20 minutes
Usual time = 20 * 3 = 60 minutes.
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NA
SHSTTON
33
Solv. Corr.
24
Solv. In. Corr.
57
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0 M:14 S
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7 / 62
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If a man walks at the rate of 5kmph, he misses a train by only 7min. However if he walks at the rate of 6 kmph he reaches the station 5 minutes before the arrival of the train.Find the distance covered by him to reach the station.
Lets assume the required distance = x km.
Difference in the times taken at two speeds=12mins=1/5 hr.
Therefore (x/5-x/6)=1/5 or (6x-5x) = 6 or x = 6km.
So required distance = 6 km
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NA
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7
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27
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34
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Yana and Gupta leave points x and y towards y and x respectively simultaneously and travel in the same route. After meeting each other on the way, Yana takes 4 hours to reach her destination, while Gupta takes 9 hours to reach his destination. If the speed of Yana is 48 km/hr, what is the speed of Gupta?
Let the speed of Yana be v1 and Gupta be v2 and time taken by them be t1 and t2 respectively.
There is a shortcut for such questions as v1^2/v2^2= t2/t1
Putting the respective values we get v2= 32km/hr
1.6 km =1 miles
So 32/1.6= 20mph.
Workspace
NA
SHSTTON
30
Solv. Corr.
6
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36
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Walking 5/6 of its usual speed, a train is 10min late. Find the usual time to cover the journey?
New speed = 5/6 of usual speed
New time = 6/5 of usual time
Therefore, (6/5 of usual time) - usual time = 10min
Therefore Usual time = 50min
Workspace
NA
SHSTTON
14
Solv. Corr.
13
Solv. In. Corr.
27
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Vivek travelled 1200km by air which formed 2/5 of his trip.One third of the whole trip , he travelled by car and the rest of the journey he performed by train. The distance travelled by tain was:
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