Paper 7 - Time ,speed and distance PDF

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Time ,speed and distance...

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2021 CA2 TSD and BOATS Test 7 Test Summary No. of Sections: 1 No. of Questions: 30 Total Duration: 40 min

Section 1 - Quants Section Summary No. of Questions: 30 Duration: 40 min

Additional Instructions: None

Q1.

A car driver travels from the plains to the hill station, which are 350 km apart at an average s covers the same distance at an average speed of 20 km/h the car. The average speed of the

20kmph

24kmph

35kmph

30kmph

Q2.

A journey of 192 km between two cities takes two hours less by a fast train than by a slow tr train is 16 km/h less than that of the fast train, then the average speed of the fast train is

40kmph

36kmph

52kmph

48kmph

14 min

24 min

32 min

46 min

Q5.

A bike rider starts at 40km/hr and he increases his speed in every 2 hours by 2km/hr. Then t in 24 hrs is:

682 km

540 km

612 km

500 km

Q6.

Ashwin has to travel from one point to another point in a certain time. Travelling at a speed o travelling at a speed of 8kmph he reaches 12 m earlier.What is the distance between this two

27 Km

18 Km

15 Km

21 Km

Q7.

A 240 metres long train crosses a platform twice its length in 36 seconds. What is the speed

65 Km/hr

130 m/sec

135 m/sec

Q9.

In a stream running at 2 km/hr, a motorboat goes 10 km upstream and back again to the sta speed (km/hr) of the motorboat in stillwater ?

17

20

22

25

Q10.

A boat can row at 16 km/hr in still water and the speed of river is 10 km/hr. Find the speed o against the river.

13 km/hr, 3 km/hr

15 km/hr, 5 km/hr

26 km/hr, 6 km/hr

6 km/hr, 26 km/hr

Q11.

A boat can travel 15 km downstream in 18 min. The ratio of the speed of the boat in still wat How much time will the boat take to cover 10 km upstream?

22 min

25 min

20 min

Q13.

A boat goes 6 km against the current of the stream in 2 hours and goes 8 km along the curre go 28.5 km in stationary water?

1 hrs

2 hrs

3 hrs

4 hrs

Q14.

A boat running downstream covers a distance of 32 km in 4 hrs and for covering the same d is the speed of the stream?

2 km/hr

3 km/hr

4 km/hr

none of the above

Q15.

A boat takes 150 min less to travel 40 km downstream than to travel the same distance upst km/hr. What is the downstream speed?

8 km/hr

10 km/hr

14 km/hr

16 km/hr

Q16.

A boat takes 25 hours for travelling downstream from point A to point B and coming back to the velocity of the stream is 5 km/hr and the speed of the boat in still water is 10 km/hr, wha

8 km/hr

10 km/hr

12 km/hr

Q18.

A man can row 6 km/hr in still water. When the river is running at 2 km/hr, it takes him 1 ½ hr far is the place?

2.5 km

4 km

5 km

10 km

Q19.

A jogger running at 9 km/h alongside a railway track in 240 meters ahead of the engine of a km/h in the same direction. In how much time will the train pass the jogger?

32 s

34 s

36 s

38 s

Q20.

Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and slower train in 36 seconds. The length of each train is:

25 m

50 m

80 Km

Q22.

The distance between two stations A and B is 450 Km. A train starts from A and moves towa Km/hr. Another train starts from B, 20 min earlier than the train A, and moves towards A at a from A will the two trains meet ?

180 Km

320 Km

190 Km

260 Km

Q23.

Two trains run to a Place at a Speeds of 45 Km/hr and 60 Km/hr respectively. If the second t train for the journey, nd the length of the journey.

600 Km

300 Km

900 Km

120 Km

Q24.

Train A travelling at 60 km/hr leaves Mumbai for Delhi at 6 p.m. Train B travelling at 90 km/h p.m. Train C leaves Delhi for Mumbai at 9 p.m. If all the three trains meet at the same time be the speed of train C if the distance between Delhi and Mumbai is 1260 km.?

120 Km/hr

150 Km/hr

160 Km/hr

140 Km/hr

Two trains A and B leaves from station a and b, respectively. They cross each other and then reach b an and 3 hours 20 minutes, respectively. What is the approximate speed of Train B, if the speed of Train A is

66 Kmph

84 Kmph

76 Kmph

54 Kmph

Q27.

Two trains one from ropar to mangalore and another from mangalore to ropar start simultan after 91 hours and 104 hours respectively.What is the ratio of their speeds?

6:7

7:6

8:7

7:8

Q28.

Bombay Express left Delhi for Bombay at 14:30 hours, travelling at the speed of 60kmph. On Delhi for Bombay at 16:30 hours at a speed of 80kmph. How far from Delhi will the two trains

480 Km

360 Km

250 Km

500 Km

Q29.

A man is walking at a speed of 9 Km/hr. After every km he takes rest for 9 min. How much ti 27 Km?

150 Km/hr

125 Km/hr

200 Km/hr

Answer Key & Solution Section 1 - Quants Q1

24kmph Solution

Avg speed = 2xy/x+y = 2(30)(20)/30+20 = 1200/50 = 24kmph

Q2

48kmph Solution

let average speed of faster train be x and slower train be x-6. From the given data, 2=(192/(x-16))-(192/x) on simplifcation x*x-16x-1536=0 x=48,-32 So average speed of train=48kmph

Q3

6: 30 am Solution

Time between 11 am and 4.30 pm = 5hrs 30min = 5.5hrs

In 5.5 hours he covered 5/6 - 3/8 of total distance

⇒ he covered 11/24 of total distance in 5.5hrs

⇒ 11/24 of total distance = 5.5 hours

Q4

14 min Solution

In both the cases the distance is same.Let the actual time be t. distance=speed *time=45(t+10/60)=60(t+4/60) on solving t=14/60 hours t=14/60 *60 minutes=14 minutes

Q5

612 km Solution

Speed of the rider: 40km/hr He increases his speed in every 1 hr by 2km/hr. Distance covered by every 1 hr will be 40,42,44….upto 12terms. i.e. (for 24hrs) Sum of 1st n terms=n/2 ( (2a+(n-1)d) 12/2 * (2*40+11*2)==>12/2 * (80+22)==>612km

Q6

21 Km Solution

D/6 – 40/60 = d/8 +12/60 d/6 – d/8 = 12/60+40/60 (8-6)d/48 = 52/60 2d/48 = 52/60

Q8

115 m/sec Solution

speed=414 km/hr To convert it into m/sec multiply it into 5/18 hence 414 *(5/18)=2070/18=115 m/sec

Q9

22 Solution

We know that time=distance/speed 10/(x-2) +10/(x+2)=55/60 55x2-1200x-220=0 x=22

Q10

26 km/hr, 6 km/hr Solution

Speed with the river (downstream) = 16+10=26 Speed against the river (upstream) = 16-10=6

Q11

20 min Solution

speed=distance/time speed (downstream)=15/(18/60)=50 km/hr From given data, speed of boat : speed of stream= 4:1

Q13

3 hrs Solution

Speed upstream = 6/2 = 3, speed downstream = 8/(1/2) = 16 Speed of boat = 1/2(3+16) = 9.5 km/hr So time in still water = 28.5/9.5=3 hrs

Q14

2 km/hr Solution

Downstream speed = 32/4 = 8 km/hr Upstream speed = 32/8 = 4 km/hr So speed of stream = 1/2*(8-4)=2

Q15

16 km/hr Solution

Let speed of boat in still water = x km/hr So speed upstream = x-4, and speed downstream = x+4 Now given: Time to travel 40 km downstream = time to travel 40 km upstream – 150/60 So 40/(x+4) = 40/(x-4) – 5/2 8/(x-4) – 8/(x+4) = 1/2 x+4 – (x-4)/(x2 – 16) = 1/16 solve, x = 12 so downstream speed = 12+4

Q16

150 km Solution

Downstream speed = 10+5 = 15 Upstream speed = 10-5 = 5 Now total time is 25 hours If distance between A and B is d, then distance BC = d/2

Solution

let x be the distance x/(6-2)+x/(6+2)=3/2 x/4+x/8=3/2 x=4 km

Q19

36 s Solution

speed=distance/time time=(240+120)/(36*5/18) =360/10 =36 sec

Q20

50 m Solution

Let the length of the train be 'x'. From the given data relative speed=46-36=10 km/hr 10*5/18=2x/36 x=50

Q21

120 Km Solution

Distance travelled by the train moving from A in 1/2 hour= 40 Km Now the distance of(220- 40)= 180 km will be covered by a relative speed of (80 + 100)= 180 Km/hr H

ti

t k

i

ti

b t

i t A

dB

180/180 1 h

= 190 Km

Q23

900 Km Solution

Let the distance be 'x' Km Time taken by First Car= x/45 Time taken by Second Car= x/60 Given, (x/45) - (x/60)= 5 x= 900 Km

Q24

120 Km/hr Solution

from the given data ,train A would have covered 180 kms by 9 p.m now A &B are travelling in the same direction at different speeds Relative speed =distance /time=>time=180/30=6 hours So the B has travelled 6*90=540 kms. It is given that C also meet them A &B at the same point . hence C has covered the remaining distance (1260-540)=720 km in 6 hours speed of C=720/6=120 km/hr

Q25

1.20 Solution

Since 8:00 to 11:00 no distance travel by train from B to A. So for 3 hours train from A travel distance distance=210km we will use relativity. So relative speed of A and B=60+30= 90km/hr

Time taken by train B to move from b to a = 3 hours 20 minutes,

= 10 / 3 hours,

Speed of train A = 80 kmph,

Suppose,

Speed of train B = x,

Since,the distance is same,

Hence,

80 * 7 / 2 = x * 10 / 3,

Or,

x = 84 kmph,

So,

Speed of train B = 84 kmph.

Q27

8:7

Let,Bombay express be B and Rajdhani express be R. Now,R starts after two hours of B starting from Delhi.So,B would have covered 60*2=120Km. When,R starts from Delhi,the distance between R and B is 120Km. Let's assume after x distance, the two trains would meet. It means B would cover x distance and R would cover (120+x),so that R meets B. Time taken by B to cover x Km=x/60 hr. Time taken by R to cover (120+x) Km=(120+x)/80 hr. Now both the times are same. So, (120+x)/80=x/60. Solving for x,we get x=360 Km. Thus the total distance from Delhi would be 360+120=480 Km.

Q29

6 hours 54 min Solution

Since he is taking a rest after every one Km. Therefore time consumed in taking Rest in 27 km = 26*9= 234 min= 3.9 hours Time taken to cover 27 km without rest= 3 hours Total time taken= 3 + 3.9= 6.9 hours= 6 hours 54 min

Q30

150 Km/hr Solution

Let the train takes 'x' hours to cover a distance of 300 Km. Then, {300/x} = {300/(x-1)} - 50 300/(x-1) - 300/x= 50 Solving the equation, we get x= 3 hours...