Q1. The average speed of a car is 1 (4/5) times the average speed of a bus. A tractor covers 575 km in 23 hours. How much distance will the car cover in 4 hours if the speed of the bus is twice speed of the tractor?
(a) 340 km
(b) 480 km
(c) 360 km
(d) 450 km
(e) None of these
S1. Ans.(c)
Sol. Average speed of a tractor = 25 km / h
The speed of a bus in an hour = 25 × 2 = 50 km
The speed of a car in an hour = 9/5 * 50 = 90 km
So, the distance covered by car in 4 h is
90 × 4 = 360 km
Q2. A bike covers a certain distance at the speed of 64 km/h in 8 hours. If the bike was to cover the same distance in approximately 6 hours, at what approximate speed should the bike travel?
(a) 80 km/h
(b) 85 km/h
(c) 90 km/h
(d) 75 km/h
(e) 70 km/h
S2. Ans.(b)
Sol. Total distance = 64 × 8 = 512 km
Now speed = 512/6 = 85.34 km/ h
Q3. The ratio between the speed of a train and a car is 16 : 15 respectively. Also, a bus covered a distance of 480 km in 8 h. The speed of the bus is three-fourth the speed of the train. How much distance will the car cover in 6 h?
(a) 450 km
(b) 480 km
(c) 360 km
(d) Cannot be determined
(e) None of these
S3. Ans.(a)
Sol. Speed of bus = 480/8 = 60km/ h
Speed of train = (60*4)/3=80 km / h
Speed of train : Speed of car = 16 : 15
Speed of car =80/16 * 15 = 75 km/ h
Distance covered by car in 6 hr = 75 × 6 = 450 km
Q4. Car A runs at the speed of 65 km/h and reaches its destination in 8h. Car B runs at the speed of 70 km/h and reaches its destination in 4h. What is the respective ratio of distances covered by Car A and Car B?
(a) 11 : 7
(b) 7 : 13
(c) 13 : 7
(d) 7 : 11
(e) None of these
S4. Ans.(c)
Sol. Distance travelled by Car A = 65 × 8 = 520 km
Distance travelled by Car B = 70 × 4 = 280 km
Ratio = 520/280 = 13 : 7
Q5. A bus started its journey from Ramgarh and reached Devgarh in 44 min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5 km/hr, how much time will it take to cover the same distance?
(a) 40 min
(b) 38 min
(c) 36 min
(d) 31 min
(e) 49 min
S5. Ans.(a)
Sol. Distance between Ramgarh and Devgarh =(50*44)/60=110/3
Average speed of the bus is increased by 5 km/hr then the
speed of the bus = 55 km/hr
Required time = 110/3*60/55 = 40 min
Q6. The wheel of an engine 4 (2/7) metres in circumference makes seven revolutions in 4 seconds. Find the speed of the train in km per hour.
(a) 27
(b) 30
(c) 33
(d) 36
(e) None of these
S6. Ans(a)
Sol. Distance covered in 4 seconds =30/7*7 metres
Speed in m/s = 30/4
Speed in km/hr = 30/4*18/5= 27 km/hr
Q7. A man takes 6 hrs 30 min in walking to a certain place and riding back. He would have gained 2 hrs 10 min by riding both ways. How long would he take to walk both ways?
(a) 8 hr 30 min
(b) 8 hr 40 min
(c) 8 hr 50 min
(d) 9 hr
(e) None of these
S7. Ans.(b)
Sol. Walking + Riding = 6 hrs 30 min ……(1)
2 Riding = 6 hrs 30 min – 2 hrs 10 min
= 4 hrs 20 min ……(2)
Solving the above two relations (equations);
2 × (1) – (2) gives
2 walking = 13 hrs – 4 hrs 20 min = 8 hrs 40 minutes
Q8. A Train which travels at the uniform rate of 10 m a second leaves Madras for Arconum at 7 a.m. At what distance from Madras will it meet a train which leaves Arconum for Madras at 7.20 a.m., and travels one-third faster than the former does, the distance from Madras to Arconum being 68 km?
(a) 40
(b) 38
(c) 36
(d) 34
(e) None of these
S8. Ans.(c)
Sol. S1 = 10 * 18/5 = 36 km/hr
S2 = 36 + 36/3 = 48 km/hr
Difference in time = T1 – T2 = 7 am – 7.20 am = 1/3 hr
Distance of meeting point from madras
Q9. A, B and C can walk at the rates of 3, 4 and 5 km an hour respectively. They start from Poona at 1, 2, 3 o’clock respectively. When B catches A, B sends him back with a message to C. When will C get the message?
(a) 5.15
(b) 5.20
(c) 5.30
(d) 6.00
(e) None of these
S9. Ans.(a)
Sol. Speed Starting time
A takes a lead of 3 km from B.
Relative speed of A and B = 4 – 3 = 1 km/hr
B catches A after 3/1 = 3 hrs, i.e., at 2 + 3 = 5 o’clock.
A returns at 5 o’clock and from a distance of 3 × 4 = 12 km from Poona.
In the meantime C covers a distance of 5 × 2 = 10 km from Poona.
Thus, A and C are 12 – 10 = 2 km apart at 5 O’clock.
Relative speed of A and C = 3 + 5 = 8 km/hr.
Thus, they meet after 2/8 = 1/4 hr = 15 min.
Thus, C will get the message at 5.15 o’clock.
Q10. Two men start together to walk a certain distance, one at 3 (3/4) km an hour and the other at 3 km an hour. The former arrives half an hour before the latter. Find the distance.
(a) 7 km
(b) 7.5 km
(c) 8 km
(d) 8.5 km
(e) None of these
Q11. A motor car does a journey in 10 hours, the first half at 21 km per hour, and the rest at 24 km per hour. Find the distance.
(a) 224 km
(b) 234 km
(c) 236 km
(d) 240 km
(e) None of these
Q12. A person going from Pondicherry to Ootacamond travels 120 km by steamer, 450 km by rail and 60 km by horse transit. The journey occupies 13 hours 30 minutes, and the rate of the train is three times that of the horse transit and 1 1/2 times that of the steamer. Find the rate of the train.
(a) 30 km/hr
(b) 60 km/hr
(c) 80 km/hr
(d) 90 km/hr
(e) None of these
Q13. How many seconds will a train 60 m in length, travelling at the rate of 42 km an hour, rate to pass another train 84 m long, proceeding in the same direction at the rate of 30 km an hour?
(a) 42
(b) 43.2
(c) 45
(d) 50
(e) None of these
Q14. A train 75 metres long overtook a person who was walking at the rate of 6 km an hour, and passed him in 7(1/2) seconds. Subsequently it overtook a second person, and passed him in 6 (3/4) seconds. At what rate was the second person travelling?
(a) 2 km/h
(b) 3 km/h
(c) 5 km/h
(d) 6 km/h
(e) None of these
15. A train takes 5 seconds to pass an electric pole. If the length of the train is 120 metres, the time taken by it to cross a railway platform 180 metres long is _______ seconds.
(a) 12.5
(b) 13.5
(c) 14.5
(d) 15.5
(e) None of these
S15. Ans(a)
Sol. Speed of the train = 120/5 = 24 m/s
time taken by the train to pass the platform
=(120+180)/24=12.5 seconds
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