IPPB Scale-1 Officer Prelims 2017 - Day 7 (Time & Distance)

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1. Two trains crosses each other in 14 sec when they are moving in opposite direction, and when they are moving in same direction they crosses each other in 3 minute 2 sec. Find the speed of the faster train by what percent more than the speed of the slower train ?

A. 18.67%
B. 16.67%
C. 20.67%
D. 23.67%
E. None of these

Sol. Let sum of length of both trains = L
And speed be = x & y.
According to the question,
L/(x-y) = 182
L/(x+y) = 14

Solving, x = 7y/6
Required % = [(7-6)/6]*100 = 16.67%.

2. 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. 54
B. 55
C. 50
D. 48
E. None of these

Sol. Sol. Lets assume train A’s speed be ’a’
And train B’s speed be ’b’
Then, b/a = √(24/5)/(10/3) = √72/50 = √36/25 = 6/5.
b = 45×6/5 = 54 km/hr.

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?

A. 5pm
B. 6pm
C. 7pm
D. 8pm
E. None of these

Sol. In one hour thief will travel 75 km.
Now let after x distance thief get caught, then
x/75 = (75+x)/100
Solving,  we get x = 225.
So to travel 225 + 75 = 300 km by police, he will take 3 hours i.e at 7 pm.

4. Tina starts running 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 ?

A. 125
B. 225
C. 250
D. 150
E. None of these

Sol. D = 20×3/2 = 30 km.
So side of square is 15km.
Area = 15² = 225 km².

5. 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 ?

A. 33 km/hr
B. 66 km/hr
C. 99 km/hr
D. 55 km/hr
E. None of these

Sol. Sol. Sound travels at 330m/sec. 
In 1 minute sound travel = 330×60 m
So, speed of the train = 330×60/720 = 330/12 m/sec = 99 km/hr.

6. A boat can travel 15 km downstream in 18 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 10 km upstream?

A. 22 min
B. 25 min
C. 20 min
D. 33 min
E. 30 min

Sol. B = [tu + td] / [tu – td] ×R
15 km downstream in 18 min so 10 km in (18/15)×10=12 min
B= 4x, R = X
Now
4x = [tu + 12] / [tu – 12] ×X
Solve, tu = 20 min.

7. A boat takes 25 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 5 km/hr and the speed of the boat in still water is 10 km/hr, what is the distance between A and B? 

A. 100 km
B. 122 km
C. 146 km
D. 178 km
E. 150 km

Sol. 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
Now distance/speed = time, so
d/15 + (d/2)/5= 25
Solve, d = 150 km.

8. A boat takes 150 min less to travel 40 km downstream than to travel the same distance upstream. The speed of the stream is 4 km/hr. What is the downstream speed? 

A. 16 km/hr
B. 12 km/hr
C. 10 km/hr
D. 8 km/hr
E. None of these

Sol. 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 = 16 km/hr.

9. It takes five times as long to row a distance against the stream as to row the same distance in favor of the stream. What is the ratio of the speed of the boat in still water to that of stream? 

A. 7 : 4
B. 2 : 3
C. 9 : 5
D. 3 : 2
E. 5 : 2

Sol. B = [tu + td] / [tu – td] ×R
So
B =[5x + x] / [5x- x] ×R
So B/R = 6/4 = 3/2.

10. In a stream running at 2 km/hr, a motorboat goes 10 km upstream and back again to the starting point in 55 minutes. Find the speed (km/hr) of the motorboat in still water.

A. 17
B. 20
C. 22
D. 25
E. None of these

Sol. Distance = time ×[B²-R²]/2×B
10 =55/60 ×[B²-2²]/2×B
Solving, B = 22 km/hr.



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