### TIME AND DISTANCE QUIZ 001

- Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively. If they cross each other in 23 seconds, what is the ratio of their speeds?

(a) Insufficient data

(b) 3 : 1

(c) 1 : 3

**(d) 3 : 2 **

(e) None of these

Explanation:

Let the speed of the trains be x and y respectively

Length of train1 = 27x

Length of train2 = 17y

Relative speed= x+ y

Time taken to cross each other = 23 s

=> (27x + 17 y)/(x + y) = 23

=> (27x + 17 y) = 23(x + y)

=> 4x = 6y

=> x/y = 6/4 = 3/2

- A train starts from Delhi at 6.00 a.m. and reaches Meerut at 10 a.m. The other train starts from Meerut at 8 a.m. and reaches Delhi at 11.30 a.m. If the distance between Delhi and Meerut is 200 km, then at what time did the two trains meet each other?

**(a) 8.56 a.m **

(b) 8.46 a.m

(c) 7.56 a.m

(d) 8.30 a.m

(e) None of these

Explanation:

The Speed of the train starting from Delhi = 200/4 = 50 km/h

The Speed of train starting from Meerut = 200/3.5 = 400/7 km/h

Suppose the two trains meet x hours after 6.00 am

Then x X 50 + (x – 2) x 400/7 = 200

or, 350x + 400x – 800 = 1400

or, 750x = 2200

or, x = 2200/750 = 2h 56 min

Hence, the required time = 8.56 am

- A train does a journey without stopping in 8 hours. If it had traveled 5 km an hour faster, it would have done the journey in 6 hours 40 min. What is its slower speed?

(a) 35 kmph

**(b) 25 kmph **

(c) 40kmph

(d) 30 kmph

(e) None of these

Explanation:

Let its slower speed = V km per hour

Here distance is same in both the cases

Using the formula = V1 x t1 = V2 x t2

or, V x 8 = (V + 5) x 20/3

or, 24V = (V + 5) x 20

V= 25 km/h

Thus, Slower speed of train is 25 km/h.

- A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?

**(a) 81 km/hr **

(b) 88 km/hr

(c) 62 km/hr

(d) 46 km/hr

(e) None of these

Explanation:

Let x is the length of the train in meter and y is its speed in kmph

x/8.4 = (y – 4.5)(10/36) —(1)

x/8.5 = (y – 5.4)(10/36) —(2)

Dividing 1 by 2

8.5/8.4 = (y – 4.5)/ (y – 5.4)

=> 8.4y – 8.4 × 4.5 = 8.5y – 8.5 × 5.4

0.1y = 8.5 × 5.4 – 8.4 × 4.5

=> .1y = 45.9 – 37.8 = 8.1

=> y = 81 km/hr

- A man covered a certain distance at some speed. If he had moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. What is the the distance in km?

(a) 36

(b) 38

**(c) 40**

(d) 42

(e) None of these

Explanation:

Let the distance be x km, the speed in which he moved = v kmph

Time taken when moving at normal speed – time taken when moving 3 kmph faster = 40 minutes

=> (x/v) – (x/(v+3)) = 40/60

⇒2v(v+3)=9x…………….(Equation1)

Time taken when moving 2 kmph slower – Time taken when moving at normal speed = 40 minutes

=> (x/ (v-2)) – (x/v) = 40/60

⇒v(v−2)=3x…………….(Equation2)

Eq 1/ Eq 2 = 2(v+3)/ (v – 2) = 3

⇒2v+6=3v−6⇒v=12

Substituting this value of v in Equation 1⇒2×12×15=9x

Hence distance = 40 km

- The speed of a bus increases by 2 km after every one hour. If the distance travelling in the first one hour was 35 km. what was the total distance travelled in 12 hours?

(a) 422km

**(b) 552km**

(c) 502km

(d) 492km

(e) None of these

Explanation:

Given that distance travelled in 1st hour = 35 km

and speed of the bus increases by 2 km after every one hour

Hence distance travelled in 2nd hour = 37 km

Hence distance travelled in 3rd hour = 39 km

Total Distance Travelled = [35 + 37 + 39 + … (12 terms)]

This is an Arithmetic Progression(AP) with first term, a=35, number of terms, n = 12 and common difference, d=2.

Hence, [35+37+39+… (12 terms)]=S12=12/2[2×35+(12−1)2]=6[70+22]=6×92=552

Hence the total distance travelled = 552 km

- Two trains A and B, 100 m long are moving on parallel tracks at speeds of 20 m/s and 30 m/s respectively. They are travelling in opposite direction. The driver of train A sees the driver of train B when he is closest to high. He throws a ball at a speed of 2 m/s which hits the tail of train B. What is the distance between the two trains?

(a) 0 m

(b) 10 m

**(c) 4 m**

(d) 8 m

(e) 5 m

Explanation:

Since the trains are travelling in opposite direction velocity for the driver of the faster train = 50 m/s

Distance travelled = length of the train = 100 m

Time taken by the ball from one train to the other = 100/50 = 2 seconds

Ball in thrown at 2 m/s, distance between the two trains = 2 × 2 = 4 m.

- Two trains, A and B, start from stations X and Y towards each other, they take 4 hours 48 minutes and 3 hours 20 minutes to reach Y and X respectively after they meet if train A is moving at 45 km/hr., then the speed of the train B is

(a) 60 km/hr

(b) 64.8 km/hr

**(c) 54 km/hr**

(d) 37.5 km/hr

(e) None of these

Explanation:

- An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 (2/3) hours, it most travel at a speed of:

(a) 300 kmph

(b) 360 kmph

(c) 600 kmph

**(d) 720 kmph**

(e) None of these

Explanation:

Distance = 240 X 5= 1200 km.

- A train is travelling at 48 kmph. It crosses another train having half of its length, travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. What is the length of the platform?

(a) 500 m

(b) 360 m

(c) 480 m

**(d) 400 m**

(e) 450 m

Directions (11): The ratio of time taken by Hunny and Bunny to swim a certain distance downstream in a river is 3 : 4 respectively. The time taken by Bunny to cover a certain distance upstream is 50% more than the time taken by him to cover the same distance downstream.

- What is the ratio of speed of Hunny to that of Bunny?

**(a) 7 : 5**

(b) 7 : 9

(c) 2 : 5

(d) 6 : 7

(e) None of these

Explanation:

Let, speed of Hunny be ‘a ’

Speed of Bunny be ‘b ’

And speed of stream be ‘r ’,

- Both of them hired a boat that runs with a speed equal to the sum of their individual speeds. If Hunny can cover a straight path of length 14 km in 60 minutes, then find the time taken by both of them to travel a distance of 48 km to and fro by the hired boat?

(a) 5 (4/143) hr.

(b) 2 (4/143) hr.

(c) 3 (4/143) hr.

**(d) 4 (4/143) hr.**

(e) None of these

Explanation:

- Two ship travelling at 30 km/hr and 90 km/hr head directly towards each other, they are 120 km apart at the starting time. How far apart are they (in Km.) at one minute before they collide.

(a) 1 km

**(b) 2 km**

(c) 3 km

(d) 4 km

(e) None of the above

Explanation:

If the final one minute before collision, the two ship

- A, B and C start from the same place and travels in same direction at speeds of 20, 30 and 40 km/hr respectively. B starts 3hour after A. If B and C overtake A at the same instant. How many hours after A did C start.

(b) 3.25

**(c) 4.5**

(d) 5.5

(e) None of the above

Explanation:

Speed of A, B and C are 30 km/hr, 40 km/hr and 60 km/hr respectively.

B Start when A already travelled for 3 h and covered

= 3 × 20 = 60 km

It means when B overtake A, A has travelled for 9 hr and B for 6 hr.

It is given that B and C overtake A at a same instance, It means when C overtakes A, both of them will have covered the same distance.

Let C takes hours to cover the same as covered by A in 9 hr.

9*20= t*40

t= 4.5

C started after (9 – 4.5 = 4.5), when A started.

- There is from point A and finish at the same point after touching points B, C and D. You, then drive 20 km interior towards the tree from point A and from there, reach somewhere in between B and C on

the ring road. How much distance do you have to travel from the tree to reach the point between B and C on the ring road?

(a) 80 km

(b) 15 m

**(c) 20 km**

(d) 40 m

Explanation:

- Published in TIME AND DISTANCE