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QUESTION: 1

Sofi started travelling from a place A to B and Priya started travelling from a place B to A which are 576 km apart. They meet after 12 hours. After their meeting, Sofi increased her speed by 2 km/hr and Priya reduced her speed by 2 km/hr, they arrived at B and A respectively at the same time. What is their initial speed?

Solution:

Sum of their speeds = Distance/time = 576/12 = 48 kmph

Respective Speed of Sofi and Priya = (25 + 23) = 48 kmph

QUESTION: 2

A and B set out at the same time to walk towards each other respectively from a place P and Q 144 km apart. A walks at the constant speed of 8 km/h, while B walks 4 km in the first hour, 5 km in the second hour, 6 km in the third hour and so on. Then the “A” will meet “B” at?

Solution:

Distance travelled by them in first hour = 12 km

Distance travelled by them in second hour = 13 km and so on

In 9 hours both will cover exactly 144 km.

In 9 hours each will cover half the total distance.

QUESTION: 3

Two Vans start from a place with a speed of 50 kmph at an interval of 12 minutes. What is the speed of a car coming from the opposite direction towards the place if the car meets the vans at an interval of 10 minutes?

Solution:

50*12/60 = 10/60 * (50+x)

600 = 500 + 10x

x = 10 kmph

QUESTION: 4

A car travels from a place A to B in 7 hour. It covers half the distance at 30 kmph and the remaining distance at 40 kmph, what is the total distance between A and B?

Solution:

Total Distance = x

(x/2*30) +(x/2*40) = 7

x = 240

QUESTION: 5

Two persons A and B start from the opposite ends of a 450 km straight track and run to and from between the two ends. The speed of the first person is 25 m/s and the speed of other is 35 m/s. They continue their motion for 10 hours. How many times did they pass each other?

Solution:

First person speed = 25 m/s * 18/5 = 90 kmph

Second person speed = 35 m/s * 18/5 = 126 kmph

First person covers 90 * 10 = 900km

900/450 = 2

QUESTION: 6

A truck travelled to a place Q from P, the first 50 km at 10 kmph faster than the usual speed, but it returned the same distance at 10 kmph slower than usual speed. If the total time taken by the truck is 12 hours, then how many hours will travel at the faster speed?

Solution:

Total time taken,

[50/(x-10)] + 50/(x +10)] = 12 hours.

By solving the equation, we get

x = 15

Time is taken by the truck at faster speed = 50/(15+10) = 2 hours.

QUESTION: 7

Mr.Kavin walks at 4/5 of his normal speed and takes 60 minutes more than the usual time. What will be the new time taken by Mr. Kavin?

Solution:

4/5 of speed = 5/4 of original time

5/4 of original time = original time + 60 minutes;

1/4 of original time = 60 minutes;

Thus, original time = 60*4 = 240 minutes = 240 + 60 = 300 minutes

QUESTION: 8

A travel bus normally reaches its destination at 60 kmph in 20 hours. Find the speed of that travel bus at which it travels to reduce the time by 5 hours?

Solution:

60 * 20 = x *15

x = 80 kmph

QUESTION: 9

A Lion starts chasing a Giraffe. It takes 4 hours to catch the Giraffe. If the speed of the Lion is 40 km/h. What is the speed of Giraffe?

Solution:

Giraffe Speed = x Kmph

4 = 4*x/(40-x)

x = 20 km/h.

QUESTION: 10

Anu and Purvi are running on a circular track of length 500m. The Speed of Anu is 40 m/s and that of Purvi is 30 m/s. They start from the same point at the same time in the same direction. When will they meet again for the first time?

Solution:

Time = Distance/Relative Speed = 500/10 = 50 s

QUESTION: 11

A boat takes 28 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 6km/hr and the speed of the boat in still water is 9 km/hr, what is the distance between A and B?

Solution:

Downstream speed = 9+6 = 15

Upstream speed = 9-6 = 3

Now total time is 28 hours

If distance between A and B is d, then distance BC = d/2

Now distance/speed = time, so

d/15 + (d/2)/3 = 28

Solve, d = 120 km

QUESTION: 12

Speed of a man in still water is 5 km/hr and the river is running at 3km/hr. The total time taken to go to a place and come back is 10 hours. What is the distance travelled?

Solution:

Down speed = 5+3 = 8

Up speed = 5-3 = 2

Let distance travelled = X

(X/8)+(X/2) = 10

X= 16 km

Total distance is 16+16 = 32

QUESTION: 13

A boat running upstream takes 9 hours 48 minutes to cover a certain distance, while it takes 7 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?

Solution:

Distance covered upstream in 9hrs 48 min = Distance covered downstream in 7hrs

(X-Y) 49/5 = (X+Y)7

X/y = 1/6

QUESTION: 14

A boat can travel 20 km downstream in 24 min. The ratio of the speed of the boat in still water to the speed of the stream is 4 : 1. How much time will the boat take to cover 15 km upstream?

Solution:

Down speed = 20/24*60 = 50km/hr

4:1 = 4x:x

Downstream speed = 4x+x = 5x

Upstream speed = 4x-x = 3x

5x = 50; x = 10

so up speed 3*10 = 30

Time = 15/30*60 = 30min.

QUESTION: 15

A boat whose speed in 20 km/hr in still water goes 40 km downstream and comes back in a total of 5 hours. The approx. speed of the stream (in km/hr) is:

Solution:

Let the speed of the stream be x km/hr. Then,

Speed downstream = (20 + x) km/hr,

Speed upstream = (20 – x) km/hr.

40/20+x + 40/20-x = 5

X = 9 approx

QUESTION: 16

A boat covers a certain distance downstream in 2 hour, while it comes back in 2 1/2 hours. If the speed of the stream be 5 kmph, what is the speed of the boat in still water?

Solution:

Let the speed of the boat in still water be *x* kmph. Then,

Speed downstream = (*x* + 5) kmph,

Speed upstream = (*x* – 5) kmph.

(*x* + 5)*2 = (*x* – 5)*5/2

X = 45 kmph

QUESTION: 17

A boat running downstream covers a distance of 40 km in 5 hrs and for covering the same distance upstream it takes 10 hrs. What is the speed of the stream?

Solution:

Downstream speed = 40/5 = 8 km/hr

Upstream speed = 40/10 = 4 km/hr

So speed of stream = 1/2*(8-4)

QUESTION: 18

A boat goes 4 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 15 km in stationary water?

Solution:

Rate downstream = 1/10 * 60 = 6kmph

Rate upstream = 4 km/hr.

Speed in still water = ½ * 10 = 5 kmph

Required time = 15/5 = 3 hr

QUESTION: 19

A man rows to a place 40 km distant and come back in 9 hours. He finds that he can row 5 km with the stream in the same time as 4 km against the stream. The rate of the stream is:

Solution:

Speed downstream = 5/x

Speed upstream = 4/x

40/(5/x) + 40/(4/x) = 9

X = ½

So, Speed downstream = 10 km/hr, Speed upstream = 8 km/hr.

Rate of the stream = 1/2 * 2 = 1 kmph

QUESTION: 20

A man can row 8 km/hr in still water. When the river is running at 4 km/hr, it takes him 2 1/3hr to row to a place and come back. How far is the place?

Solution:

Downstream speed = 8+4 = 12 ⇒ a

Upstream speed = 8-4 = 4 ⇒ b

Distance = a*b/(a+b) * total time (t)

= 12*4/16 * 7/3

= 7kms

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