Quiz 2

Question 1

Answer the questions on the basis of the information given below. Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed. At what time do Ram and Shyam first meet each other?

10:00 a.m.

16.18%

10:30 a.m.

38.97%

10:20 a.m.

19.85%

10:10 a.m.

25%

  • PrepInsta Explanation
  • User Explanation

Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed. Ram starts at 9:00 am and Shyam starts at 9:45 am from A. Ram reaches B at 10:00 am (as his speed is 5km/hr and the distance between A and B is 5km) When Ram reaches B, Shyam is 15/60 × 10 = 2.5 km away from A. Ram meets Shyam (2.5 × 60)/(10 + 5) minutes after 10:00 a.m. i.e., at 10:10 a.m. Shyam reaches B at 10:15 a.m. At 10:15 a.m., Ram is (15/60) × 5 = 1.25 km away from B. Shyam overtakes Ram in 1.25/(10 – 5) = 0.25 hrs = 15 minutes after 10:15 am i.e. at 10:30 a.m. 

Hence, option 2.

Question 2

At what time does Shyam overtake Ram?

10:20 a.m.

8.89%

10:30 a.m.

71.11%

10:40 a.m

14.81%

10:50 a.m.

5.19%
  • PrepInsta Explanation
  • User Explanation

Shyam overtakes Ram at 10:30 a.m.

Hence, option 2.

Question 3

Only a single rail track exists between station A and B on a railway line. One hour after the north bound superfast train N leaves station A for station B, a south passenger train S reaches station A from station B. The speed of the superfast train is twice that of a normal express train E, while the speed of a passenger train S is half that of E. On a particular day N leaves for station B from station A, 20 minutes behind the normal schedule. In order to maintain the schedule both N and S increased their speed. If the superfast train doubles its speed, what should be the ratio (approximately) of the speed of passenger train to that of the superfast train so that passenger train S reaches exactly at the scheduled time at the station A on that day

1:5

16.36%

1:2

36.36%

1:3

31.82%

1:6

15.45%
  • PrepInsta Explanation
  • User Explanation

initial ration is 1:4 because, E/2 divided by 2E we get, the same.
now, we know dist/speed=time.Form an eq. with this formula:-
so from the ratio 4x is the speed of superfast train and x is the speed of pass.train
D/4X (Time taken by superfast train) + D/X (Time taken by pass.train) = 60min
solving we get,
D/X =48, means that Time taken by pass.train is 48 mins.
12mins for superfast train.

For 20 mins later schedule,
superfast will double its speed, so it takes on 12/2 = 6mins.
Bal.14mins remains behind schedule.
48-14=34mins, means pass.train covering distance.
Final ratio=6:34 = 1:6 (round off 5.6)

Question 4

On a straight road XY, 100 metres in length, 5 stones are kept beginning from the end X. The distance between two adjacent stones is 2 metres. A man is asked to collect the stones one at a time and put at the end Y. What is the distance covered by him?

460 metres

22.03%

540 metres

20.34%

860 metres

45.76%

920 metres

11.86%
  • PrepInsta Explanation
  • User Explanation

The first stone is kept at X and the subsequent stones are kept at a uniform distance of 2 metres from each other.

  • The total distance covered by the man to keep all the stones at Y = 100 + 2 × (98 + 96 + 94 + 92)  = 100 + 2 × (380) = 860 metres

Hence, option 3.

Question 5

On a 20km tunnel connecting two cities A and B there are three gutters. The distance between gutter 1 and 2 is half the distance between gutter 2 and 3. The distance from city A to its nearest gutter, gutter 1 is equal to the distance of city B from gutter 3. On a particular day the hospital in city A receives information that an accident has happened at the third gutter. The victim can be saved only if an operation is started within 40 minutes. An ambulance started from city A at 30 km/hr and crossed the first gutter after 5 minutes. If the driver had doubled the speed after that, what is the maximum amount of time the doctor would get to attend the patient at the hospital? Assume 1 minute is elapsed for taking the patient into and out of the ambulance.

4 minutes

28.57%

2.5 minutes

28.57%

1.5 minutes

25.51%

Patient died before reaching the hospital

17.35%
  • PrepInsta Explanation
  • User Explanation

As per the description,

AB = 20 km

AG1 = BG3

2G1G2 = G2G3

Also,

x = 2.5 km

y + 2y = 20 − 2x

y = 5 km

Time to cover A to G

While coming back his speed is 60 km/hr.

Time taken to cover the distance from G3 to A  

(i.e. 17.5 km) = 17.5 minutes

Required time = 20 + 17.5 + 1 = 38.5 minutes

The doctor will have 1.5 minutes to attend the patient.

Hence, option 3 is correct.

Question 6

Inside the tunnel is a cat located at a point that is 3/8 of the distance AB measured from the entrance A. When the train whistles, the cat runs. If the cat moves to the entrance of the tunnel A, the train catches the cat exactly at the entrance. If the cat moves to the exit B, the train catches the cat exactly at the exit. The speed of the train is greater than the speed of the cat by what order ?

4:1

34.02%

1:2

25.77%

8:1

21.65%

None of these

18.56%
  • PrepInsta Explanation
  • User Explanation

 

Let the speed of the train be St and the speed of the CAT be Sc.

Case 1:

The CAT runs towards the train.

Case 2:

The CAT runs away from the train.

Equating (i) and (ii),

St : Sc = 4 : 1  

Hence, option 1 is the correct one..

or

Let ‘c’ and ‘t’ be the velocity of train and cat.
Get the diagram right (if diagram is required)

1st case :
Train and cat meet at point A in the diagram.
Let train be at a distance of “y” from the entrance of the tunnel.
Cat is at a distance of 3x/8 from the entrance of the tunnel (Cat is between A&B. i.e. 3x/8 from A and 5x/8 from B )
So, by the time train runs a distance of y, cat runs a distance of 3x/8 (As they reach entrance at the same time)
Hence, equating the time taken, we have, y/t = 3x/8c

2nd case:
Train and cat meet at point B in the diagram.
Train travels a distance of y + x (Till the end of the tunnel)
Cat travels a distance of 5x/8 (Till the end of the tunnel)
Both reach at the same time, hence we can equate the time. We get, y + x/t = 5x/8c.

Subtracting the 2 equations, we have, (2nd case – 1st case) :
[(y +x)/t] – [y/t] = (5x/8c) – (3x/8c)
x/t = 2x/8c
c/t = 1/4.
t/c = 4/1.

Question 7

In a 4000 meter race around a circular stadium having a circumference of 1000 meters, the fastest runner and the slowest runner reach the same point at the end of the 5th minute, for the first time after the start of the race. All the runners have the same starting point and each runner maintains a uniform speed throughout the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken by the fastest runner to finish the race?

20 min

19.35%

15 min

26.88%

10 min

44.09%

25 min

9.68%
  • PrepInsta Explanation
  • User Explanation

Let the speed of the slowest runner be s m/min and the speed of the fastest runner be 2s m/min. Length of the race track = 1000 m and the two runners meet after 5 minutes.

Relative speed = 1000/5 = 200 m/min

2s − s = 200

s = 200 m/min

  • The speed of the fastest runner = 2s = 400 m/min

The time taken by the fastest runner to complete the race = 4000/400 = 10 min

Hence, option 3

 

The slowest runner covers 500 m when the fastest runner covers 1000 m.

The two meet at the starting point when the fastest runner covers 2000 m and the slowest runner covers 1000 m.

  • The fastest runner runs 2000 m in 5 minutes.

He runs 4000 m in 10 minutes.

Hence, option 3 is the correct one.

Question 8

Arun, Barun and Kiranmala start from the same place and travel in the same direction at speeds of 30, 40 and 60 km per hour respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start?

3

18.68%

3.5

15.38%

4

53.85%

4.5

6.59%

5

5.49%
  • PrepInsta Explanation
  • User Explanation

Arun has travelled 60 km when Barun starts.

Barun overtakes Arun in 60/(40 – 30) = 6 hrs

In this time, Barun travels 6 × 40 = 240 km from the starting point.

Kiranmala overtakes Arun at the same point.

Kiranmala takes 240/60 = 4 hrs to reach there.

Arun takes 240/30 = 8 hrs to reach there.

∴ Kiranmala starts 8 – 4 = 4 hrs after Arun.

Hence, option 3.

Question 9

A father and his son are waiting at a bus stop in the evening. There is a lamp post behind them. The lamp post, the father and his son stand on the same straight line. The father observes that the shadows of his head and his son's head are incident at the same point on the ground. If the heights of the lamp post, the father and his son are 6 metres, 1.8 metres and 0.9 metres respectively, and the father is standing 2.1 metres away from the post, then how far (in metres) is the son standing from his father?

0.9

17.86%

0.75

27.38%

0.6

27.38%

0.45

27.38%
  • PrepInsta Explanation
  • User Explanation

Let F stands for father and S stands for a 18/0.9
y ? n + y = 2y

son.

Question 10

Karan and Arjun run a 100-metre race, where Karan beats Arjun by 10 metres. To do a favour to Arjun, Karan starts 10 metres behind the starting line in a second 100-metre race. They both run at their earlier speeds. Which of the following is true in connection with the second race?

Karan and Arjun reach the finishing line simultaneously.

33.7%

Arjun beats Karan by 1 metre.

19.57%

Arjun beats Karan by 11 metres.

14.13%

Karan beats Arjun by 1 metre.

32.61%
  • PrepInsta Explanation
  • User Explanation

If Karan runs 100m then Arjun runs 90 metres. So, their speeds are in the
ratio of 10 : 9.
Now, if Karan runs 110 m then Arjun runs 99m. Ans.(4)

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