1. Two horses start trotting towards each other, one from A to B and another from B to A. They cross each other after one hour and the first horse reaches B, 5 /6 hour before the second horse reaches A. If the distance between A and B is 50 km. What is the speed of the slower horse?
(a) 30 km/h
(b) 15 km/h
(c) 25 km/h
(d) 20 km/h
(e) none of these
(e) none of these
2. Pankaj walked at 5 km/h for certain part of the journey and then he took an auto for the remaining part of the journey travelling at 25 km/h. If he took 10 hours for the entire journey, what part of journey did he travelled by auto if the average speed of the entire journey be 17 km/h :
(a) 750 km
(b) 100 km
(c) 150 km
(d) 200 km
(e) none of these
3. Two trains A and B start simultaneously in the opposite direction from two points P and Q and arrive at their destinations 16 and 9 hours respectively after their meeting each other. At what speed does second train B travel if the first train travels at 120 km/h per hour:
(a) 90 km/h
(b) 160 km/h
(c) 67.5 km/h
(d) 80 km/h
(e) none of these
(e) none of these
4. Abhinav started for the station half a km from his home walking at 1 km/h to catch the train in time. After 3 minutes he realised that he had forgotten a document at home and returned with increased, but constant speed to get it succeded in catching the train. Find his latter speed in km/h:
(a) 1.25
(b) 1.1
(c) 11/9
(d) 2
(e) none of these
(e) none of these
5. Train X starts from point A for point B at the same time that train Y starts from B to A. Point A and B are 300 km apart. The trains are moving at a constant speed at least at 25 km/h. The trains meet each other 3 hours after they start. If the faster trains takes at least 2 more hours to reach the destination. By which time will the slower train have definitely reached its destination? (Ignoring the length of trains in crossing)
(a) 4 hours after the start
(b) 7.5 hours after the start
(c) 6 hours after the start
(d) 7 hours after the start
(e) none of these
(e) none of these
6. In reaching the Purnagiri a man took half as long again to climb the second third as he did to climb the first third and a quarter as long again for the last third as for the second third. He took altogether 5 hs 50 minutes. Find the time he spent on the first third of the journey?
(a) 72 min
(b) 80 min
(c) 81 min
(d) 88 min
(e) none of these
(e) none of these
7. A boat covers 48 km upstream and 72 km downstream in 12 hours, while it covers 72 km upstream and 48 downstream in 13 hours. The speed of stream is :
(a) 2 km/h
(b) 2.2 km/h
(c) 2.5 km/h
(d) 4 km/h
(e) none of these
8. A motor boat takes 2 hours to travel a distance of 9 km downstream and it takes 6 hours to travel the same distance against the current. The speed of the boat in still water and that of the current (in km/h) respectively are :
(a) 6, 5
(b) 3, 1.5
(c) 8, 5
(d) 9, 3
(e) none of these
(e) none of these
9. A coolie standing on a railway platform observes that a train going in one direction take 4 seconds to pass him Another train of same length going in opposite direction takes 5 seconds to pass him. The time taken (in seconds) by the two trains to cross each other will be :
(a) 35
(b) 36.5
(c) 40/9
(d) 45
(e) none of these
(e) none of these
10. Pushpak express leave Lucknow at 6 am and two hours later another train Bhopal express leaves Lucknow. Both trains arrive Bhopal at 4 pm on the same day. If the difference between their speeds be 10 km/h, what is the average speeds of both the trains over entire route :
(a) 40 km/h
(b) 44(4/9) km/h
(c) 42(3/5) km/h
(d) 43 km/h
(e) none of these
(e) none of these
Answers
1.(D)
Let speed of faster horse = x
& speed of slower horse = y
x + y = 50/1
x + y = 50 ---- (I)
50/y – 50/x = 5/6 ---- (II)
With the help of option
x = 30 kmph
y = 20 kmph
2.(C)
Total distance = 17*10=170
Let Journey travelled by auto in x hr
25 * x + (10-x ) 5 = 170
25 x + 50 – 5x = 170
x = 6
Required Ans = 6 * 25 = 150 km
3.(B)
S1/S2 = (9/16)^1/2
S1/S2 = ¾
3 = 120
4 = 160
4.(C)
Distance covered in 3 minute = 3*(1000/60) = 50
Now he has to cover (500+50) meters in (30-3) minutes
Required speed = (550/1000)/(27/60) = 11/9 km/h
5.(B)
Let Speed of train x = a kmph
& Speed of train y = b kmph
a + b = 300/3 = 100 kmph
The faster trains takes be atleast = (3+2) hr = 5 hr
i.e speed of slower train = 40 kmph
i.e time = 300/40 = 7.5 hr
6.(B)
Let the time token in first third part of the Journey be x minute, then the required in second third part of the Journey is 3x/2 & in the last third part of the Journey time required is 15x/8
i.e x+3x/2+15x/8=350 min
x = 80 min
7.(A)
From 1st condition
48/u+72/d = 12 ---- (I)
72/u+48/d = 13 ---- (II)
From eq (I) & (ii)
u = 8 kmph
d = 12 kmph
Speed of streem = (12-8)1/2 = 2 kmph
8.(B)
D = 9/2 = 4.5 kmph
U = 9/6 = 1.5 kmph
x = (4.5+1.5) 1/2 = 3.5 kmph
y = (4.5-1.5)1/2 = 1.5 kmph
9.(C)
Let speed of 1st train = x m/s
& speed of other train = y m/s
(d/x)/(d/y) = 4/5
y/x = 4/5
Required time = (d+d)/(x+y)
= (4x+5y)/(x+y)
=( 4*5+5*4)/(4+5) = 40/9
10.(B)
Let speed of 1st train = x kmph
& speed of 2nd train = (x+10) kmph
So,
X*10 = (x+10) 8
X= 40 kmph
Required Average speed = (2*40*50)/(40+50) = 44(4/9)
