Time and Distance and Time and work (UPSC) Part-II

Total Questions: 32

11. A daily train is to be introduced between station A and station B starting from each at 6 AM and the journey is to be completed in 42 hours. What is the number of trains needed in order to maintain the Shuttle Service? [2016-II]

Correct Answer: (c) 4
Solution:

Above given figures show that train 1 leaves station A on 1st day and train 2 leaves station B on 1st day. Both the trains don’t reach their destination even on the 2nd day after 24 hours as the journey completes in 42 hours.
∴ Two more trains need to be introduced at both the stations i.e., station A and B. So, 4 trains are needed in order to maintain the shuttle service.

12. A freight train left Delhi for Mumbai at an average speed of 40 km/hr. Two hours later, an express train left Delhi for Mumbai, following the freight train on a parallel track at an average speed of 60 km/hr. How far from Delhi would the express train meet the freight train? [2017-II]

Correct Answer: (c) 240 km
Solution:

Distance travelled by freight train in 2 hour = 2 × 40 = 80 km.
Relative speed = 60 km/hr - 40 km/hr = 20 km/hr
Hence, time taken by express train to meet
Freight train = 80 km / 20 km/hr = 4 hr.

So, Distance travelled = 4 × 60 or 6 × 40 = 240 km.

13. Average hourly earnings per year (E) of the workers in a firm are represented in figures A and B as follows: [2018-II]

From the figures, it is observed that the

Correct Answer: (c) slopes of the graphs are same
Solution:We can see from graph slopes of both graphs are same

14. The figure drawn below gives the velocity graphs of two vehicles A and B. The straight line OKP represents the velocity of vehicle A at any instant, whereas the horizontal straight line CKD represents the velocity of vehicle B at any instant. In the figure, D is the point where perpendicular from P meets the horizontal line CKD such that PD = ½ LD : [2018-II]

What is the ratio between the distances covered by vehicles A
and B in the time interval OL?

Correct Answer: (c) 3 : 4 
Solution:Required Ratio = 1/2(PL) . (OL)/(OC) . (OL) = PL/2(OC)

=PL/2 × 2/3PL = 34/4 = 3: 4

15. A train 200 metres long is moving at the rate of 40 kmph. In how many seconds will it cross a man standing near the railway line?    [2018-II]

Correct Answer: (d) 18
Solution:Length of train = distance = 200 m

Speed of train = 40 × 5/18 = 100/9 m/s

Required time = 200 ÷ 100/9 = 18 sec

16. Two persons, A and B are running on a circular track. At the start, B is ahead of A and their positions make an angle of 30° at the centre of the circle. When A reaches the point diametrically opposite to his starting point, he meets B. What is the ratio of speeds of A and B, if they are running with uniform speeds?     [2018-II]

Correct Answer: (a) 6 : 5
Solution:B is 30° head to A
Total angle covered by A = 180°
Total angle covered by B = 180° - 30° = 150°
Required ratio = 180° : 150° = 6 : 5

17. When a runner was crossing the 12 km mark, she was informed that she had completed only 80% of the race. How many kilometres was the runner supposed to run in this event?    [2019-II]

Correct Answer: (b) 15
Solution:Let the runner suppose to run n km.
then, n × 80/100 = 12 ⇒ n = 12 × 100/80 = 15 km.

18. X, Y and Z are three contestants in a race of 1000 m. Assume that all run with different uniform speeds. X gives Y a start of 40 m and X gives Z a start of 64 m. If Y and Z were to compete in a race of 1000 m, how many metres start will Y give to Z?                                  [2019-II]

Correct Answer: (b) 25
Solution:x gives y a start of 40 m.
x gives z a start of 64 m.
Let they all complete the race in t hours

So, x's speed = 1000/t ⇒ y's speed = 960/t

z's speed = 936/t

Again, Let y gives z a start of x m.

1000 × t/960 = (1000-x)/936 ⇒ 25 = (1000-x)/39

x = 1000 - 975 = 25m.

19. A person X can complete 20% of work in 8 days and another person Y can complete 25% of the same work in 6 days. If they work together, in how many days will 40% of the work be completed? [2020-II]

Correct Answer: (a) 6
Solution:X can complete 20% of work in 8 days.
So, X can complete 100% of work in 8 × 5 = 40 days.
Again, Y can complete 25% of work in 6 days.
So, Y can complete 100% of work in 6 × 4 = 24 days
Time required to complete whole work by working together
= 40 × 24 / 40 + 24 = 40 × 24 / 64 = 15 days.

Now, time required to complete 40% of the work
= 40/100 × 15 = 6 days.

20. A car travels from a place X to place Y at an average speed of v km/hr, from Y to X at an average speed of 2v km/hr, again from X to Y at an average speed of 3v km/hr and again from Y to X at an average speed of 4v km/hr. Then the average speed of the car for the entire journey [2020-II]

Correct Answer: (b) lies between v and 2v km/hr
Solution:Let the distance between X and Y is d Km.
Average Speed = Total distance covered / Total time taken
= (d + d + d + d) / (d/v + d/2v + d/3v + d/4v)
= 4d × 12v / (12 + 6 + 4 + 3)d = 4 × 12v / 25
= 1.92v Km/hr.
Hence, average speed lies between v and 2v Km/hr.