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1. The Sinhagad Express left Pune at noon sharp. Two
hours later, the Deccan Queen started from Pune in the same direction. The Deccan Queen overtook the
Sinhagad Express at 8 p.m. Find the average speed of the two trains over this journey if the sum of their
average speeds is 70 km/h.

Correct Answers :

[A]

Explanation :

The ratio of time for the travel is 4:3 (Sinhagad to Deccan Queen). Hence, the ratio of speeds would be 3:4. Since, the sum of their average speeds is 70 kmph, their respective speeds would be 30 and 40 kmph respectively. Use alligation to get the answer as 34.28 kmph.

2. Walking at 3/4 of his normal speed, Abhishek is 16
minutes late in reaching his office. The usual time taken by him to cover the distance between his home
and his office is

Correct Answers :

[A]

Explanation :

When speed goes down to three fourth (i.e. 75%)
time will go up to 4/3^{rd} (or 133.33%) of the original time. Since, the extra time required is 16 minutes, it
should be equated to 1/3^{rd} of the normal time. Hence, the usual time required will be 48 minutes.

3. Ram and Bharat travel the same distance at the rate
of 6 km per hour and 10 km per hour respectively. If Ram takes 30 minutes longer than Bharat, the
distance travelled by each is

Correct Answers :

[C]

Explanation :

Since, the ratio of speeds is 3:5, the ratio of times would be 5:3. The difference in the times would be 2 (if looked at in the 5:3 ratio context.) Further, since Ram takes 30 minutes longer, 2 corresponds to 30. Hence, using unitary method, 5 will correspond to 75 and 3 will correspond to 45 minutes. Hence at 10 kmph, Bharat would travel 7.5 km.

4. Two trains for Mumbai leave Delhi at 6 : 00 a.m. and
6 : 45 a.m. and travel at 100 kmph and 136 kmph respectively. How many kilometres from Delhi will
the two trains be together?

Correct Answers :

[C]

Explanation :

The train that leaves at 6 am would be 75 km ahead of
the other train when it starts. Also, the relative speed being 36 kmph, the distance from Mumbai would be:

(75/36) X 136 = 283.33 km

5. Two trains, Calcutta Mail and Bombay Mail, start
at the same time from stations Kolkata and Mumbai respectively towards each other. After passing each
other, they take 12 hours and 3 hours to reach Mumbai and Kolkata respectively. If the Calcutta Mail is
moving at the speed of 48 km/h, the speed of the Bombay Mail is

Correct Answers :

[D]

Explanation :

If you assume that the initial stretch of track is covered
by the two trains in time t each, the following figure will give you a clearer picture.

From the above figure, we can deduce that, t/3 = 12/t.

Hence, t2 = 36, gives us t = 6.

Hence, the distance between Kolkata to the starting point is covered by the Calcutta Mail in 6 hours,
while the same distance is covered by the Bombay Mail in 3 hours.

Hence, the ratio of their speeds would be 1:2. Hence, the Bombay Mail would travel at 96 kmph.

6. Shyam’s house, his office and his gym are all equidistant
from each other. The distance between any 2 of them is 4 km. Shyam starts walking from his gym
in a direction parallel to the road connecting his office and his house and stops when he reaches a point
directly east of his office. He then reverses direction and walks till he reaches a point directly south of his
office. The total distance walked by Shyam is

Correct Answers :

[D]

Explanation :

From the figure above we see that Shyam would have walked a distance of 4 + 4 + 4 = 12 km. (G to P1,
P1 to G and G to P2).

7. Lonavala and Khandala are two stations 600 km
apart. A train starts from Lonavala and moves towards Khandala at the rate of 25 km/h. After two
hours, another train starts from Khandala at the rate of 35 km/h. How far from Lonavala will they will
cross each other?

Correct Answers :

[C]

Explanation :

When the train from Khandala starts off, the train
from Lonavala will already have covered 50 kms.

Hence, 550 km at a relative speed of 60 kmph will
take 550/60 hrs. From this, you can get the answer as: 50 + (550/60) * 25 = 279.166 km.

8. Walking at 3/4 of his normal speed, a man takes
2(1/2) hours more than the normal time. Find the normal time.

Correct Answers :

[A]

Explanation :

9^{6} When his speed becomes 3/4th, his time would
increase by 1/3rd. Thus, the normal time = 7.5 hrs.
(since increased time = 2.5 hrs).

9. Alok walks to a viewpoint and returns to the starting
point by his car and thus takes a total time of 6 hours 45 minutes. He would have gained 2 hours by
driving both ways. How long would it have taken for him to walk both ways?

Correct Answers :

[A]

Explanation :

Since he gains 2 hours by driving both ways (instead of walking one way) the time taken for driving would be 2 hours less than the time taken for walking. Hence, he stands to lose another two hours by walking both ways. Hence his total time should be 8 hrs 45 minutes.

10. Sambhu beats Kalu by 30 metres or 10 seconds. How
much time was taken by Sambhu to complete a race 1200 meters.

Correct Answers :

[A]

Explanation :

Kalu’s speed = 3 m/s. For 1200 m, Kalu would take 400 seconds and Sambhu would take 10 seconds less. Hence, 390 seconds.

11. What is the time taken by Chandu to cover a distance
of 360 km by a motorcycle moving at a speed of 10 m/s?

Correct Answers :

[A]

Explanation :

Since Chandu is moving at a speed of 10 m/s and he has to cover 360 km or 360000 meters, the time taken would be given by 360000/10 seconds = 36000 seconds = 36000/60 minutes = 600 minutes = 10 hours.

12. Without stoppage, a train travels a certain distance
with an average speed of 60 km/h, and with stoppage, it covers the same distance with an average speed
of 40 km/h. On an average, how many minutes per hour does the train stop during the journey?

Correct Answers :

[A]

Explanation :

Since the train travels at 60 kmph, it’s speed per minute is 1 km per minute. Hence, if it’s speed with stoppages is 40 kmph, it will travel 40 minutes per hour.

13. Rajdhani Express travels 650 km in 5 h and another
940 km in 10 h. What is the average speed of train?

Correct Answers :

[C]

Explanation :

Total distance/Total time = 1590/15 = 106 kmph.

14. Rishikant, during his journey, travels for 20 minutes
at a speed of 30 km/h, another 30 minutes at a speed of 50 km/h, and 1 hour at a speed of 50 km/h and
1 hour at a speed of 60 km/h. What is the average velocity?

Correct Answers :

[A]

Explanation :

The distance covered in the various phases of his
travel would be:

10 km + 25 km + 50 km + 60 km.

Thus the total
distance covered = 145 km in 2 hours 50 minutes →145 km in 2.8333 hours → 51.18 kmph

15. A car travels from *A* to *B* at *V*_{1} km/h, travels back
from *B* to *A* at *V*_{2} km/h and again goes back from *A* to *B* at *V*_{2} km/h. The average speed of the car is:

Correct Answers :

[C]

Explanation :

The average speed would be given by:

16. Narayan Murthy walking at a speed of 20 km/h
reaches his college 10 minutes late. Next time he increases his speed by 5 km/h, but finds that he is
still late by 4 minutes. What is the distance of his college from his house?

Correct Answers :

[D]

Explanation :

By increasing his speed by 25%, he will reduce his time by 20%. (This corresponds to a 6 minute drop in his time for travel—since he goes from being 10 minutes late to only 4 minutes late.) Hence, his time originally must have been 30 minutes. Hence, the required distance is 20 kmph × 0.5 hours = 10 km.

17. Jayshree goes to office at a speed of 6 km/h and
returns to her home at a speed of 4 km/h. If she takes 10 hours in all, what is the distance between
her office and her home?

Correct Answers :

[A]

Explanation :

d/6 + d/4 = 10 → d = 24 km.

18. A motor car does a journey in 17.5 hours, covering
the first half at 30 km/h and the second half at 40 km/h. Find the distance of the journey.

Correct Answers :

[B]

Explanation :

If the car does half the journey @ 30 kmph and
the other half at 40 kmph it’s average speed can be estimated using weighted averages.

Since, the distance traveled in each part of the journey is equal, the ratio of time for which the car
would travel would be inverse to the ratio of speeds.

Since, the speed ratio is 3:4, the time ratio for the two halves of the journey would be 4:3. The average
speed of the car would be:

(30 x 4 + 40 x 3)/7 = 240/7 kmph.

It is further known that the car traveled for 17.5

hours (which is also equal to 35/2 hours).

Thus, total distance = average speed x total time = (240 x 35)/(2 x 7) = 120 x 5 = 600 km

19. Sujit covers a distance in 40 minutes if he drives at a speed of 60 kilometer per hour on an average. Find the speed at which he must drive at to reduce
the time of the journey by 25%?

Correct Answers :

[D]

Explanation :

To reduce the time of the journey by 25%, he should increase his speed by 33.33% or 1/3rd. Thus, required speed = 80 kmph.

20. Manish travels a certain distance by car at the rate of
12 km/h and walks back at the rate of 3 km/h. The whole journey took 5 hours. What is the distance he
covered on the car?

Correct Answers :

[A]

Explanation :

You can solve this question using the options. Option (a) fits the given situation best as if we take the distance as 12 km he would have taken 1 hour to go by car and 4 hours to come back walking—a total of 5 hours as given in the problem.

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