Aptitude - Time and Distance
11.
A thief steals a car at 1:30 p.m. and drives it at 40 kmph. The theft is discovered at 2 p.m. and the owner sets off in another car at 50 kmph. He will overtake the thief at :
Answer
Distance covered by thief in 30 min = 20 km.
Clearly, 20 km is compensated by owner at a relative speed of 10 kmph in 2 hrs. So, he overtakes teh thief at 4 P.M.
Answer :
Option BExplanation :
Distance covered by thief in 30 min = 20 km.
Clearly, 20 km is compensated by owner at a relative speed of 10 kmph in 2 hrs. So, he overtakes teh thief at 4 P.M.
12.
The speeds of three cars are in the ratio 2 : 3 : 4. The ratio of the times taken by these cars to travel the same distance is :
Answer
Ratio of time taken = 12 : 13 : 14 = 6 : 4 : 3
Answer :
Option DExplanation :
Ratio of time taken = 12 : 13 : 14 = 6 : 4 : 3
13.
A bullock cart has to cover a distance of 80 km in 10 hrs. If it covers half of the journey in 35th of the time, what would be its speed to cover the remaining distance in the time left ?
Answer
Distance left = 802 km = 40 km.
Time left =
1 − 35 
x 10 
hrs = 25 x 10 hrs = 4 hrs.
Speed required = 404 kmph = 10 kmph
Answer :
Option CExplanation :
Distance left = 802 km = 40 km.
Time left =
1 − 35 x 10 hrs = 25 x 10 hrs = 4 hrs.Speed required = 404 kmph = 10 kmph
14.
A walks at a uniform rate of 4 km an hour and 4 hrs after his start, B cycles after him at the uniform rate of 10 kmph. How far from the starting point will B catch A ?
Answer
Suppose B catches A after x hrs. Then,
distance travelled by A in (x + 4)hrs = distance travelled by B in x hrs.
4(x + 4) = 10x ⇒ 6x = 16 ⇒ 3x = 8
⇒ x = 83 hrs
Distance travelled by B in 83 hrs = 83 x 10 km = 26.7 km
Answer :
Option DExplanation :
Suppose B catches A after x hrs. Then,
distance travelled by A in (x + 4)hrs = distance travelled by B in x hrs.
4(x + 4) = 10x ⇒ 6x = 16 ⇒ 3x = 8
⇒ x = 83 hrs
Distance travelled by B in 83 hrs =
83 x 10 km = 26.7 km 15.
A takes 2 hrs more than B to walk d km. If A doubles his speed then he can make it in 1 hour less than B. How much time does B require for walking d km ?
Answer
Suppose B takes x hrs to walk d km.
Then, A takes (x + 2) hrs to walk d km.
with double of the speed, A will take 12 (x + 2) hrs
∴ x − 12 (x + 2) = 1 ⇒ 2x − (x + 2) = 2 ⇒ x = 4
Hence B takes 4 hours to walk d km.
Answer :
Option DExplanation :
Suppose B takes x hrs to walk d km.
Then, A takes (x + 2) hrs to walk d km.
with double of the speed, A will take 12 (x + 2) hrs
∴ x − 12 (x + 2) = 1 ⇒ 2x − (x + 2) = 2 ⇒ x = 4
Hence B takes 4 hours to walk d km.
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