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QUESTION: 1

Excluding stoppages, a train can travel with a speed of 60km/hr but with stoppages it can travel at an average 45km/hr. For how many minutes the train stops in one hour.

Solution:

due to stoppages 15km less is travel by train so,

15 = 60*t, t = 15 minutes – train stops in one hour

QUESTION: 2

Two trains are travelling towards each other. The distance between the trains initially is 400km. After some time they meet at a distance of 150 km from one end. Find the ratio of the speed of the trains.

Solution:

At some tine T they meet each other so,

150/a = 250/b (a and b are the speeds of the train respectively)

So, a:b = 3:5

QUESTION: 3

A thief steals a car at 3 pm and drives at 75 km/hr. He got discovered by the police at 4 pm Then the police start chasing him in another car travelling at 100km/hr. When will the policeman catch the thief?

Solution:

In one hour thief will travel 75 km. Now let after x distance thief get caught, then

x/75 = (75+x)/100

u will get x = 225, so to travel 225 + 75 = 300 km by police, he will take 3 hours i.e at 7 pm

QUESTION: 4

A journey of 800 km is done in a total of 10 hours, If 320 km is travel by train and remaining by bus. The same journey is done in 8 hours if 240 km is travel by train and remaining is done by bus. Find the ratio of the speed of train to bus.

Solution:

10 = 320/st + 480/sb and

8 = 240/st + 560/sb

st and sb are the speeds of train and bus respectively

QUESTION: 5

If a man walks to his office at 5km/hr, he will be late by 30 minutes. If he walks at 6km/hr, he will belate by 10minutes. Find the distance between his home and office?

Solution:

Let distance be D km, then,

D = 5*(t + 1/2) and D = 6*(t+ 1/6) solve both question and we get D = 10km

QUESTION: 6

Rakesh travelled 1800 kilometre by air which formed 3/5 of the total journey. He travels 1/4 of the trip by car and the remaining trip by train. Find the distance travelled by train.

Solution:

3/5 of D = 1800. So D = 3000 km,

so distance travelled by train = 3000 – 1800 – 1/4 of 3000 = 450

QUESTION: 7

Arya starts cycling along the boundaries of the squares. She starts from a point A and after 90 minutes she reached to point C diagonally opposite to A. If she is travelling with 20km/hr, then find the area of square field.

Solution:

D = 20*3/2 = 30 km. So side of square is 15km, so area – 225km^{2}

QUESTION: 8

The distance between two cities P and Q is 300km. A train starts from station P at 10 am with speed 80 km/hr towards Q. Another train starts from Q towards P with speed 40km/hr at 11 am. At what time do they meet?

Solution:

First train starts at 10am so in one hour it covers 80 km in one hour. Now distance b/w P and Q is 220. Suppose at some’ x’ km they meet. So,

x/80 = (220-x)/40

x = 440/3. The time after which they meet = (440/3)/80 = 11/6 i.e = 1hr 50 min.

QUESTION: 9

A walks with a speed of 6 km/hr and after 5 hr of his start, B starts running towards A at a speed of 8 km/hr. At what distance from start will B catch A.

Solution:

In 5hrs, A will cover 30 km. Now, at some distance ‘x’. So A will cover X distance and B will cover 30 + X.

x/6 = (30+x)/8

x = 90. So distance from start after which B will catch A = 120km

QUESTION: 10

Two guns were fired from the same place at an interval of 13 minutes but a person travelling in a train approaching the place hear the second sound after 12 minutes than the first. Find the speed of the train. Consider sound travels at a speed of 330 meter per sec.

Solution:

Sound travels at 330m/sec. In one minute sound travel = 330*60 meter.

So speed of train = (330*60)/720 = 330/12 m/sec or 330/12 of 18/5 = 99 km/hr

QUESTION: 11

A train 150 meters of length travels at the rate of 60 km/hr. In what time the train will pass a man who is walking at a speed of 10 km/hr in opposite direction.

Solution:

150 = (70)*5/18*t

QUESTION: 12

Two trains of length 100 meter and 125 meter are travelling at a speed of 45 km/hr and 60km/hr respectively in same direction. In what time they will completely cross each other.

Solution:

225 = (60 – 45)*5/18*T

QUESTION: 13

Two trains are travelling in same direction with 60 km/hr and 75 km/hr respectively. The faster train crosses a man sitting in the slower train in 30 sec. find the length of faster train.

Solution:

L = 15*5/18*30 = 125 meter

QUESTION: 14

A train running at 45 km/hr takes 36 sec to pass a platform. Next, the train takes 12 sec to pass a man walking at the speed of 15 km/hr in the same direction. Find the length of the platform.

Solution:

Let ‘T’ and ‘P’ are the length of train and platform respectively

T = 12*30*5/18 = 100 meter

P + 100 = 45*5/18*36

P= 350

QUESTION: 15

Two stations P and Q are 400 km apart from each other. One train start from P at a speed of 60km/hr towards Q and after 2 hours another train starts from Q towards P at 45 km/hr. At what distance from P the train will meet.

Solution:

First train will travel 120 km before the start of second train, Now the distance between them is 280km.

Now, x/60 = (280 – x)/45

We get x = 160 km, so distance from P = 120 + 160 = 280 km

QUESTION: 16

Two stations A and B are 150 km apart from each other. One train starts from A at 6 AM at a speed of 30 km/hr and travels towards B. Another train starts from station B at 7 AM at a speed of 20 km/hr. At what time they will meet.

Solution:

Distance travel by first train in one hour = 30, now the distance remains 120 km only.

x/30 = (120 – x)/20, so we get x = 72 km

Now, time = (30 + 72)/30 = 3hrs and 24minutes i.e. 9: 34 am

QUESTION: 17

Two trains of length 120 meter and 150 meter crosses a stationary man in 10 and 15 seconds respectively. In what time they will cross each other when they are moving in same direction.

Solution:

120 = a*10, a = 12 m/sec (speed of first train)

150 = b*15, b = 10 m/sec (speed of second train)

270 = (2)*T, T = 135 seconds

QUESTION: 18

A train running with 72km/hr takes 20sec to cross a platform 200 m long. How much it takes to cross a stationary train having twice the length of platform.

Solution:

200+L = 72*(5/18)*20. L= 200m.

400 + 200 = 72*(5/18)*t. So, t = 30sec

QUESTION: 19

A train travelling with 54 km/hr takes 20 second to cross a bridge. Another train 70 meter shorter crosses the same bridge at 36 km/hr. Find the time taken by the second train to cross the bridge.

Solution:

Let L and B are length of train and bridge respectively.

L + B = 54*5/18*20 = 300 meter

L + B – 70 = 36*5/18*t = 230, se we get t = 23 sec

QUESTION: 20

Two trains are moving in opposite direction having speed in the ratio 5:7. First train crosses a pole in 12 second and second train crosses the same pole n 15 second. Find the time in which they can cross each other completely.

Solution:

Let the length of first train and second train be a and b meter. Then

a = 5x*12 = 60x and b = 7x*15 = 105x

They are moving in opposite direction, 165x = (12x)*T

T = 165/12 = 55/4 sec

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