1.A car completes a journey in 10 hours, if it covers half of the journey at 40 km/hr and the remaining at 60 km/hr. The distance covered by car is:
(a) 400 km
(b) 480 km
(c) 380 km
(d) 300 km
(e) None of the above
Let the total distance covered by car = 2d
According to question total time = 10hr
d/40+d/60=10
5d/120=10
d = 240
2d = 480 km
2.A bus meets with an auto at 10:00 am while going the same way in the same direction towards Haridwar. The Bus reach at Haridwar at 12:30 p.m. and take 1 hour rest at there. Bus return on the same way and meet with the same auto half an hour later. At what time the auto will reach at Haridwar?
(a) 3 pm
(b) 4 pm
(c) 3:30 pm
(d) 5 pm
(e) None of the above
Let C is point where the auto and the bus meet first time and D is a point where the auto and the
Bus meet 2nd time.
According to the above diagram:
Distance C D covered by Bus in 2 hour and auto covered the same distance in 4 hr.
Distance C B covered by Bus 2.5 hr
And by Auto in double of Bus = 2.5 × 2 = 5 hour
Time = 10 + 5 = 3 pm
3.In covering a distance of 30 km, Arun takes 2 hours more than Sumit. If Arun doubles his speed, then he would take 1 hour less than Sumit. Arun’s speed in (km/hr) is:
(a) 5
(b) 6.25
(c) 6
(d) 7.5
(e) None of the above
Let the Arun speed is x km/hr and
Sumit speed is y km/hr
30/x¬-30/y=2 …(i)
30/y-30/2x=1 …(ii)
On adding (i) and (ii)
30/x-30/2x=3
(60-30)/2x=3
30/2x=3
x = 5 km/hr
4. A man can reach a certain place in 30 hours. If he reduces his speed by 1/15th, he goes 10 km less in that time. Find his initial speed per hour.
(a) 6 km/hr
(b) 5 1/2 km/hr
(c) 4 km/hr
(d) 5 km/hr
(e) None of the above
This speed after reduction =1-1/15=14/15
His time change =15/14
New time = 15t
Old time = 14t
14t = 30
t = 30/14
15t =30/14×15
He travels 10 km less in time =450/14-30
=(450-420)/14=30/14
His new speed = 10/30×14=14/3km/hr
Initial speed =14/3×15/14 = 5 km/hr.
5.The length of the minutes hand of a clock is 8cm. Find the distance travelled by its outer end in 15 minutes.
(a) 4 πcm
(b) 8 πcm
(c) 12 πcm
(d) 16 πcm
(e) None of the above
Distance travelled by the end of minutes hand =2πr/4
=(2 × π × 8)/4=4πcm
6.A man walked at a speed of 4 km/h from point A to B and came back from point B to A at the speed of 6 km/h what would be ratio of time taken by the man in walking from point A to B to that from point B to A:
(a) 5: 3
(b) 2: 3
(c) 3: 2
(d) 4: 3
When distance is constant
S∝1/T
S1/S2 =T2/T1
T1/T2 =6/4
T1/T2 =3/2
T1 ∶T2=3∶2
7.Two train 130 m and 110 m long, while going in the same direction. The faster train take one minute to pass the completely. If they are moving in opposite direction, they cross each other completely in 3 seconds. Find the speed of each train:
(a) 42 m/s, 38 m/s
(b) 38 m/s, 36 m/s
(c) 36 m/s, 44 m/s
(d) None of these
Let, speed of faster trim S_1 m/s
Speed of slower train =S_2 m/s
S1-S2=(130+110)/(1×60)
= 4 m/s
S1+S2=(130+110)/3=80
S1=42 m/s
S2=38 m/s
8.A boy started from his house by bicycle at 10:00 am at a speed of 12 km/h. His elder brother started after 1 hour 15 minute by scooter along the same path and caught him at 1: 30 pm. The speed of scooter was (in km/h):
(a) 4.5
(b) 36
(c) 18 2/3
(d) 9
Distance covered by cycling in 1 1/4 hr = 12 + 12×1/4 = 15 km
Elder brother catch the boy = in 2 1/4 hr
Now, according to question
(Scooter)_(Speed )-(Cycling)_Speed=15/(2 1/4)
(Scooter)_(speed )=(15 × 4)/9+12
=20/3+12
=56/3=18 2/3
9.A man is walking at a speed of 10 km/h. After every km. he takes a rest for 5 minutes. How much time will he take to cover a distance of 5 km:
(a) 60 minutes
(b) 50 minutes
(c) 40 minutes
(d) 70 minutes
Time taken in covering 5 km
=5/10=1/2 hr = 30 minutes
That person will take rest for four times.
Required time = (30 + 4 × 5) = 50 minutes
10.The fare of a bus is Rs. x for the first five kilometers and Rs 13 per km thereafter. If a passenger pays Rs. 2402 for journey of 187 km. What is the value of x?
(a) 29
(b) 39
(c) 36
(d) None of these
Required equation,
x + 182 × 13 = 2402
x = 2402 – 2366
x = 36
