Q1. If a cyclist moves 4 km/hr faster. It takes 30 minutes lesser but if he moves 2 km/hour slower it takes 20 minutes more to reach the destination. Find out the distance he traveled? Q2. In a race A gives B a start of 25m and C a start of 50m. If B runs 50% faster than C and all the three reaches the finishing point simultaneously, then find the ratio of the speeds of A and C ? Q3. A hare pursued by a greyhound, is 50 of her own leaps ahead of him. While the hare takes 4 leaps, the greyhound takes 3 leaps. In one leap, the hare goes 1.75 meters and the greyhound 2.75 meters. Find out in how many leaps will the greyhound overtakes the hare? Q4. A train takes 20 seconds to cross a cyclist moving in the same direction at 36 km/hr. If it takes 1 minute to cross a boy, sitting in another train, which is moving in the same direction at 72 km/hr, then find the speed of the train (in m/s) Q5. A man swims up stream 20 km and 30 km downstream taking 5 hours each. Find the speed of the current. Q6. The tyres of a particular type of car are known to run at a constant speed of 5 revolutions per second, irrespective of the tyre dimensions. What should be the tyre diameter if one has to cover a distance of 660 meters in one minute? Q7. The daily work of 2 men is equal to that of 3 women or that of 4 youngsters. By employing 14 men, 12 women, and 12 youngsters a certain work can be finished in 24 days. If it is required to finish it in 14 days and as an additional labour, only men are available, how many of them will be required? |
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Q1. c. 60 km
Q3. b. 210 leaps
Q5. d. 1 km/hours
Q6. a. 70 cm
Q2. In a race A gives B a start of 25m and C a start of 50m. If B runs 50% faster than C and all the three reaches the finishing point simultaneously, then find the ratio of the speeds of A and C ?
a. 2 : 1
b. 4 : 3
c. 5 : 4
d. 3 : 1
The realtive distance between Vb and Vc is 25m and the realtive speed is 50% (let it be 0.5)
Thus the time taken by Vb to cover up this distance = Total time = 25/0.5 = 50
Again,
1.5* 50 * Vc = Vc * 50 + 25
=> 75 Vc - 50 Vc = 25
=> Vc= 1
and Vb = 1.5
And 50Va = 25 + 75
=> Va = 2
So the ratio of velocities 2 : 1. ans a
Let v is the velocity
then L = length of the train = (V - 10) 20
and 20(V-10) = 60(V-20)
=>V - 10 = 3V - 60
=> V = 25 m/s (ans C)
n/a
Q7. The daily work of 2 men is equal to that of 3 women or that of 4 youngsters. By employing 14 men, 12 women, and 12 youngsters a certain work can be finished in 24 days. If it is required to finish it in 14 days and as an additional labour, only men are available, how many of them will be required?
a. 20 men
b. 18 men
c. 48 men
d. 28 men
Sol: According to question work of 3 women can be done by 2 men only.
So, Work of 12 women can be done by 8 men only.
And work of 4 youngster can be done by 2 men only.
So, work of 12 youngster can be done by 6 men only.
Let to finish the work in 14 days" a " of additional men are required.
And the work of (14 men+12 women+ 12 youngster) =work done by 28 men.
28x24=14(28+a)
Solving,a=2.
Ans: (a) 20.
n/a
Q1. If a cyclist moves 4 km/hr faster. It takes 30 minutes lesser but if he moves 2 km/hour slower it takes 20 minutes more to reach the destination. Find out the distance he traveled?
a. 55 km
b. 50 km
c. 60 km
d. 65 km
Let the initial(original) speed=s km/h
And the time=t hours.
Distance=st km....(i)
Now the speed =(s+4) and time=(t-30/60)....(ii)
And the other speed=(s-2) and time=(t+20/60)....(iii)
By equating(i) & (iii), (i) & (ii)...
We can get the solution as 60 km.
n/a
Q5. A man swims up stream 20 km and 30 km downstream taking 5 hours each. Find the speed of the current.
a. 4 km/hours
b. 3 km/hours
c. 2 km/hours
d. 1 km/hours
Sol:Let the speed of man in still water be u km/hr and the speed of current = vkm/hr.
According to question,
20/(u-v)=5 &,
30/(u+v)=5.
Solving,u=5km/hr & v=1km/hr.
Ans:(d) 1km/hr.
n/a
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