# Aptitude Logical Reasoning Time and Distance 2021 ACT Part 4

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1. A car started running at a speed of 30 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey.

A. 380 km

B. 390 km

C. 400 km

D. 410 km

E. None of these

Ans: B

Explanation:

The total distance covered by the car in the first 10 hours

= sum of 10 terms in AP whose first term is 30 and last term is 48

=

= 390 km.

2. Train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. The length of train P is three-fourths the length of train Q. What is the ratio of the speed of train P to that of train Q?

A.

B.

C.

D.

E. None of these.

Ans: A

Explanation:

Given that train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds.

Let the length of train P be and that of train Q be

given that =

As the train P and Q crosses the pole in 30 seconds and 75 seconds respectively,

➾ Speed of train

Speed of train

➾

Ratio of their speeds =

=

3. A train travelled from station P to Q in 8 hours and came back from station Q to P is 6 hours. What would be the ratio of the speed of the train while traveling from station P to Q to that from station Q to P?

A. 4: 3

B. 9: 16

C. 16: 9

D. 3: 4

E. None of these.

Ans: D

Explanation:

Since

4. By travelling at 40 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?

A. 20 kmph

B. 30 kmph

C. 25 kmph

D. 15 kmph

E. None of these.

Ans: A

Explanation:

Let the time taken to reach the destination be 3x hours.

He covered in hours So, the remaining 40x km, he has to cover in 2x hours.

Required speed = .

5. Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 2 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them?

A. 12 km

B. 20 km

C. 24 km

D. 4 km

E. None of these

Ans: B

Explanation:

=

[They are travelling in the opposite direction, relative speed sum of the speeds] .

6. A train leaves Mumbai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 50 kmph. When and at what distance from Mumbai do the two trains meet?

A. 1: 00pm, 220 km

B. 1: 00pm, 200km

C. 2: 00pm, 200 km

D. 2: 00pm, 220 km

E. None of these

Ans: C

Explanation:

When the second train leaves Mumbai the first train covers km

So, the distance between first train and second train is 40 km at 10.00am

Time taken by the trains to meet

hours

So, the two trains meet at 2 p. m. The two trains meet 4 ⚹ 50 = 200 km away from Mumbai.

7. Two trains of equal lengths are running at speeds of 30 kmph and 60 kmph. The two trains crossed each other in 30 seconds when travelling in opposite direction. In what time will they cross each other when travelling in the same direction?

A. 90 sec

B. 75 sec

C. 85 sec

D. 80 sec

E. None of these

Ans: A

Explanation:

Let the length of each train be x m.

8. A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform?

A. 44 sec

B. 49 sec

C. 42 sec

D. 47 sec

E. None of these

Ans: D

Explanation:

Let the length of the train be x m.

When a train crosses an electric pole, the distance covered is its own length.

So, m.

Time taken to cross the platform min.

9. Excluding stoppages, the average speed of a bus is 60 km/hr and including stoppages, the average speed of the bus is 40 km/hr. For how many minutes does the bus stop per hour?

A. 10

B. 12.5

C. 15

D. 20

E. Cannot be determined

Ans: D

Explanation:

In 1 hr, the bus covers 60 km without stoppages and 40 km with stoppages.

Stoppage time = time take to travel km i.e.. 20 km at 60 km/hr.

Stoppage time =

10. Train X crosses a stationary train Y in 60 seconds and a pole in 25 seconds with the same speed. The length of the train X is 300 m. What is the length of the stationary train Y?

A. 320 m

B. 420 m

C. 300 m

D. 360 m

E. None of these

Ans: B

Explanation:

Let the length of the stationary train Y be

Given that length of train X, = 300 m

Let the speed of Train X be V.

Since the train X crosses train Y and a pole in 60 seconds and 25 seconds respectively.

➾ = 25 -- ⇾ (1)

-- ⇾ (2)

From (1) V = = 12 m/sec.

From (2) = 60

Length of the stationary train = 420 m

11. In a 1000 m race, A beats B by 50 m and B beats C by 100 m. In the same race, by how many meters does A beat C?

A. 145

B. 150

C. 155

D. 160

E. None of these

Ans: A

Explanation:

By the time A covers 1000 m, B covers m.

By the time B covers 1000 m, C covers m.

So, the ratio of speeds of A and C =

So, by the time A covers 1000 m, C covers 855 m.

So in 1000 m race A beats C by m.

12. In a 1000 m race, A beats B by 200 meters or 25 seconds. Find the speed of B?

A. 8 m/s

B. 25m/s

C. 10m/s

D. 15m/s

Ans: A

Explanation:

Since A beats B by 200 m or 25 seconds, i

t implies that B covers 200 m in 25 seconds.

Hence speed of B = = 8 m/s.

13. Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time anywhere on the track if they are moving in opposite directions?

A. 21 sec

B. 24 sec

C. 25 sec

D. 27 sec

E. None of these

Ans: D

Explanation:

Time taken to meet for the first time anywhere on the track

=

=

= 27 seconds.

14. A and B go around a circular track of length 600 m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?

A. 120 sec

B. 150 sec

C. 140 sec

D. 130 sec

E. None of these

Ans: A

Explanation:

Time taken to meet for the first time at the starting point

= LCM {length of the track/speed of A , length of the track/speed of B}

=

=

= 120 sec.

15. An express travelled at an average speed of 100 km/hr, stopping for 3 min after every 75 kn. How long did it take to reach its destination 600 km from the starting point?

A. 6 hrs 21 min

B. 6 hrs 24 min

C. 6 hrs 27 min

D. 6 hrs 30 min

Ans: A

Explanation:

Time taken to cover 600 km = = 6 hrs.

Number of stoppages =

Total time of stoppages = min

Hence, total time taken = 6 hrs 21 min.

16. Anna left for city A from city B at 5.20 a. m. She travelled at the speed of 80 km/hr for 2 hrs 15 min. After that the speed was reduced to 60 km/hr. If the distance between two cities is 350 kms, at what time did Anna reach city A?

A. 9.20 a. m

B. 9.25 a. m

C. 9.35 a. m

D. 10.05 a. m

E. None of these

Ans: E

Explanation:

Distance covered in 2 hrs 15 min i.e.. , hrs = = 180 hrs.

Time taken to cover remaining distance = hrs

= = 2 hrs 50 min

.

So, Anna reached city A at 10.25 a. m.

17. A man complete a journey in 10 hrs. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km?

A. 220 km

B. 224 km

C. 230 km

D. 234 km

Ans: B

Explanation:

Let the total distance be x km.

Then,

18. A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 47 minutes. The total distance is?

A. 2

B. 3

C. 4

D. 5

Ans: B

Explanation:

Let the total distance be 3x km.

Then,

Total distance =

19. A is faster than B. A and B each walk 24 km. The sum of their speeds is 7 km/hr and the sum of times taken by them is 14 hours. Then, A՚s speed is equal to?

A. 3 km/hr

B. 4 km/hr

C. 5 km/hr

D. 7 km/hr

Ans: B

Explanation:

Let A՚s speed = x km/hr. then, B՚s speed =

So,

Since, A is faster than B, so A՚s speed = 4 km/hr and B՚s speed = 3km/hr.

20. A person travels from P to Q a speed of 40 km/hr and returns by increasing his speed by 50 % . What is his average speed for both the trips?

A. 36 km/hr

B. 45 km/hr

C. 48 km/hr

D. 50 km/hr

Ans: C

Explanation:

Speed on return trip = 150 % of 40 = 60km/hr

Average speed = .