**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)

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