Time and Distance with Explanation

Q8. Car A finishes a trip of 300 km in 7.5 hours while car B completes a trip of 450 km in 9 hours. What is the ratio of their speed?

Answer- Option B

Explanation-

Ratio of speeds =

300x

2 15

:

450 9

= 40 : 50 = 4 : 5

Q9. Arun goes to his office from his home at a rate of 3 km/hr and returns at a rate of 2 km/hr. Find the distance between his office and home, if he takes 5 hours in this entire journey?

Answer- Option D

Explanation-

Average speed =

2 x 3 x 2 3 + 2

km/hr =

12 5

km/hr

Distance travelled =

12 5

x5 = 12 km

Distance between home and office =

12 2

km = 6 km

Q10. A certain distance is traveled by truck at a certain speed. If a bus covers half the distance in double the time, find the ratio of the speed of the bus to that of the truck?

Answer- Option A

Explanation-

Let the distance covered by truck be x and the time taken be y. Then,
Required ratio =

0.5x 2y

:

x y

=

1 4

: 1 = 1 : 4

Q11. An inspector notices a thief from a distance of 200 meters after this thief starts running and the inspector chases him. The inspector and the thief run at the speed of 11 km/hr and 10 km/hr respectively. The distance between them after 6 minutes is?

Answer- Option C

Explanation-

Relative speed of the theif and inspector = (11 - 10) km/hr = 1 km/hr
Distance covered in 6 minutes =

1 x 6 60

km =

1 10

km = 100 m.

Distance between the thief and inspector = (200 - 100) m = 100 m.

Q12. A man in a plane finds that he can count 21 stars in 1 minute. Assuming the distance between stars is 50 meters, what is the speed of the plane?

Answer- Option A

Explanation-

Number of gaps between 21 stars = 20.
Distance travelled in 1 minute = (50 x 20) m = 1000 m = 1 km.
Speed = 60 km/hr.

Q13. A passionate traveler travels 100 km by car at 50 km/hr, 800 km by ship at 40 km/hr, 600 km by train at 80 km/hr and 500 km by helicopter at 400 km/hr. Find the average speed for the entire journey?

Answer- Option A

Explanation-

Total distance travelled = (600 + 800 + 500 + 100) km = 2000 km.
Total time taken =

600 80

+

800 40

+

500 400

+

100 50

hr =

123 4

hrs.

Average speed =

2000 x 4 123

km/hr = 65.04 km/hr.

Q14. A train starts from city Y at 2 PM and travels towards city X at 75 km/hr. Another train starts from city X at 1 PM and travels towards Y at 60 km/hr. If the distance is between theses two cities is 330 km then at what time will they meet?

Answer- Option D

Explanation-

Suppose they meet x hours after 1 p.m. Then,
(Distance moved by first in x hours) + [Distance moved by second in (x - 1) hrs] = 330
60x + 75 (x - 1) = 330
x = 3.
So, they meet at (1 + 3), i.e 4 p.m.