**1. 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**

**2. 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**

**3. 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**

**4. 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**

**5. 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**

**6. 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**

**7. 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**

**8. 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**

**9. 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**

**10. 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**

**Answers**

**1.(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**

**2.(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**

**3.(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**

**4.(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**

**5.(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)**

**6.(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**

**7.(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**

**8.(B)**

**S1/S2 = (9/16)^1/2**

**S1/S2 = ¾**

**3 = 120**

**4 = 160**

**9.(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**

**10.(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**

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