19. A thief is spotted by a policeman at a distance of 400 m. If the speed of the thief be 10 km/hr and that of the policeman be 12 km/hr, at what distance will the policeman catch the thief?
a. 2 km
b. 2.2 km
c. 2.4 km
d. 3 km

Answer: C

Explanation:
Formula to find time for both objects meet each other = $\displaystyle\frac{{{\text{Distance Between Objects}}}}{{{\text{Relative Speed}}}}$ = $\dfrac{{0.4}}{{12 - 10}} = 0.2$ hours.
Distance covered by police man = 0.2 × 12 = 2.4 km

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20. Two persons start walking in opposite directions at 5 km/h and 4 km/h respectively. After how many hours will they be 45 km apart?
a. 4 hrs
b. 5 hrs
c. 6 hrs
d. 8 hrs

Answer: B

Explanation:
Relative speed of two persons = 5 + 4 = 9 km/h
Therefore, Time taken = $\displaystyle\frac{{{\text{Distance Between Objects}}}}{{{\text{Relative Speed}}}}$ = $\dfrac{{45}}{{5 + 4}}$ = $\displaystyle\frac{{45}}{9}$ = 5 hours

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21. A theft is reported to a policeman. The thief starts running and the policeman chases him. When the policeman starts chasing, the thief was at a distance of 250 meters. The thief and the policeman run at the speed of 8 km/h and 9 km/h respectively. Find the time the policeman will take to catch the thief.
a. 15 minutes
b. 18 minutes
c. 20 minutes
d. 25 minutes

Answer: A

Explanation:
Formula to find time for both objects meet each other = $\displaystyle\frac{{{\text{Distance Between Objects}}}}{{{\text{Relative Speed}}}}$ = $\dfrac{{0.25}}{{9 - 8}} = 0.25$ hours or 15 minutes.

Alternative Method:
Policeman gains = (9 - 8) kmph = 1 kmph
Therefore, He will gain 250 metre in 15 minutes.
He will catch the thief in 15 minutes.

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22. The distance between two stations A and B is 220 km. A train leaves A towards B at an average speed of 80 km/hr. After half a hour, another train leaves B towards A at an average speed of 100 km/hr. Time taken for the trains to meet is:
a. 0.5 hr
b. 0.75 hr
c. 0.8 hr
d. 1 hr

Answer: D

Explanation:
Let required distance be x km.
In half an hour, Distance covered by the first train = 0.5 x 80 = 40 km.
Distance between the two trains by that time second trains starts = 220 - 40 = 180 km.
Time taken for the trains to meet = $\dfrac{{180}}{{100 + 80}}$ = 1 hr.

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23. The distance between two stations A and B is 220 km. A train leaves A towards B at an average speed of 80 km/hr. After half a hour, another train leaves B towards A at an average speed of 100 km/hr. The distance of the point where the two trains meet, from A is :
a. 120 km
b. 130 km
c. 140 km
d. 150 km

Answer: A

Explanation:
Let required distance be x km.
In half an hour, Distance covered by the first train = 0.5 x 80 = 40 km.
Distance between the two trains by that time second trains starts = 220 - 40 = 180 km.
Time taken for the trains to meet = $\dfrac{{180}}{{100 + 80}}$ = 1 hr.
Distance from A where both trains meet = Distance covered by train A in first half an hour + Distance covered in the next 1 hour = 40 + 80 = 120 km.

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24. Two trains start at the same time from Vijayawada and Madras and proceed towards each other at 16 km/hr and 21 km/hr respectively. When they meet, it is found that one train has travelled 60 km more than the other. The distance between the two stations is :
a. 445 km
b. 444 km
c. 440 km
d. 450 km

Answer: B

Explanation:
Suppose they meet after x hours.
21x - 16x= 60 or x = 12
Required distance = $(16 \times 12 + 21 \times 12)$ km = 444 km