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Chapter – 4 Tests - 3
1. Along a road lie an odd number of stones placed at intervals of 10 m. these stones have to be assembled around the middle stone. A person can carry only one stone at a time. A man carried out the job starting with the stone in the middle, carrying stones in succession, thereby covering a distance of 4.8km. then the number of stones is
2. Two trains start simultaneously, one from Mumbai to Kolkata and the other from Kolkata to Mumbai. The 2 cities are separated by a distance of 2100 km. traveling at uniform speeds; they meet at Nagpur, which ‘x’ km away from Mumbai. After meeting, the Mumbai-bound train reaches Mumbai in 7.5
d. data insufficient
3. One man can do as much work in one day as a woman can do in 2 days. A child does one-third the work in a day as a woman. If an estate owner hires 39 pairs of hands – men, women and children in the ratio 6:5:2 – and pays them in all Rs.1113 at the end of the day’s work, what must the daily wages of a child be, if the wages are proportional to the amount of work done?
4. A and B starts from x and y simultaneously and head towards y and x respectively. The ratio of their speeds is 2:1. if each one does 6 return trips (if A’s return trip is x to y; y to x) , then how many times would they met each other?
5. On return from a business trip Nawab Mohammad was to be picked up from railway station by his coachman. Somehow he managed a train connection earlier and thus arrived 2 hr too early. Immediately on arrival, he rang up home for the coach and was told that it had just left in order to be exactly in time for the train by which he was scheduled to come. To save time, he started walking homeward at 3 mph. On the way he meets the coachman who brought him home an hour before the schedule. How far is Nawab Mohammad’s house from the railway station?
a. 6 miles
b. 18 miles
d. 36 miles
6. On a straight road XY, 100m long, five heavy stones are placed 2 m apart beginning at the end X. A worker, starting at X, has to transport all the stones to Y, by carrying only one stone at a time. The minimum distance he has to travel is
a. 472 m
b. 422 m
c. 744 m
d. 860 m
7. Neeraj has agreed to mow from a lawn, which is a 20m × 40m rectangle. The mower mows 1m wide strips. If Neeraj starts at one corner and mows around the lawn toward the centre, about how many times would he go round before he was mowed half the lawn?
d. none of these
8. A train approaches a tunnel AB. Inside the tunnel is a cat located at a point that is 3/8 of the distance AB measured from the entrance A. when the train whistles the cat runs. If the cat moves to the entrance of the tunnel A, the train catches the cat exactly at the entrance. If the cat moves to the exit B, the train catches the cat at exactly the exit. The speed of the train is greater than the speed of the cat be what order?
a. 6.40 pm
b. 7 pm
c. 7.20 pm
d. 8 pm
9. It takes six technicians a total of 10 hr to build a new server from direct computer, with each working at the same rate. If 6 technicians start to build the server at 11 am, and one technician per hour is added beginning at 5 pm, at what time will the server be completed?
a. 6.4 pm
c. 7.20 pm
10. Consider a road with 2 cars at a distance of 100 km driving in the same direction. The left – side car drives at a speed of 40 km/hr and the right – side car at a speed of 60 km/hr. A bird starts from the same location as the right – side car and files at a speed of 80km/hr. When it reaches the left – side car, it turns its direction; and when it reaches the right – side car, it turns its direction again to the opposite, and so on. What is the total distance that the bird has covered at the moment the 2 cars reach each other?
11. A group of workers was put on a job. After the days work was over, one worker was withdrawn each day. The job was finished when the last worker was withdrawn. If no worker were withdrawn at any stage, the group would have finished the job in 2 – 3rd the time. How many workers were there in the group?
12. A man starts from point A and walks northwards at the speed of 6 km/hr. He then turns right and walks eastwards at the speed of 4km/hr, turns right again and walks southwards at the speed of 8km/hr and turns left and walks eastwards at the rate of 6km/hr. the time he walks in various directions is inversely proportional to the speed with which he walks. If the total distance that he covers is equal to 100 km, then find how far he is from the starting point.
d. data insufficient
13. A man can walk up in a moving escalator (upwards) in 30 s. The same man can walk down this moving ‘up’ escalator in 90 s. Assume that his walking speed is same both in upwards and downwards. How much time will he take to walk up the escalator when it is not moving?
a. 30 s
b. 45 s
c. 60 s
d. 90 s
14. A boat goes 32 km downstream and 12 km upstream in 3 ½ hr. It can 24km downstream and 28 km upstream in 5 hr. How much time will it take to cover 20 km downstream and 16 km upstream?
a. 2hr 40min
b. 4hr 10min
c. 3hr 45min
d. 3hr 15min
15. Dheeraj was walking to and fro on a railway platform. Assuming that he walks at a uniform speed of 4 km/hr in a straight path and that he reverses his direction of motion at the end of 4th, 7th, 9th and 13th minutes, how far will he be from the starting point at the end of the 10 minute?
d. 0 km
16. In a kilometer race, If A gives B a 40m start, A wins by 19 s. But if A gives B a 30 s start, B wins by 40m. Find the time taken by B to run 5000 m?
a. 150 s
b. 450 s
c. 750 s
d. 825 s
17. 2 champion swimmers start a 2- length swimming race at the same time, but from opposite ends of the pool. They swim at constant but different speeds. They first pass at a point 18.5m from the deep end. Having completed one length, each swimmer takes a rest at the edge of the pool for 45 s. After setting off on the return length, the swimmers pass for the second time just 10.5 m from the shallow end. Thus, length of the pool is
a. 90 m
b. 45 m
c. 26.5 m
d. data insufficient
18. For questions 17, the rest times given are
a. required for the calculation
b. not required at all
c. both not required but one is required
d. none of these
19. Pipe A takes 16min to fill a tank. Pipes B and C, whose cross – sectional circumference are in the ratio 2:3, fill another tan twice as big as the first. If A has a cross – sectional circumference that is one – third of C, how long will it take for B and C to fill the second tank? (Assume the rate at which water flows through a unit cross sectional area is same for all the 3 pipes)
a. 66/13 min
b. 40/13 min
c. 16/13 min
d. 32/13 min
20. The distance from the railway station to a village is 4 km. A boy and a car left the station at the same time for the village; 10 min later the boy met the car on the way back from the village. Having walked another 1/14 km he met the car once again which had arrived at the station and had again set out for the village. Find respective speeds of the boy and the car in kilometers per hour assuming them to be uniform with no stoppages.
a. 3 and 45
b. 2.5 and 40
c. 4 and 50
d. 3 and60
21. 2 guns were fired from the same place at an interval of 12 min; but a person in the train approaching the place hears the second shot 10 min after the first. The speed of the train, if speed of sound is 330 m/s; is
d. none of these
22. On a circular track of length more than 200 m, Shivku runs twice as fast as Pawan. In a running race, if Shivku gives a lead of 100 m to Pawan, when will they meet for the first time? When will they meet for the first time if the length of the track is only 150 m?
a. 150 m, 90 m
b. 250 m, 75m
c. 200 m, 50m
d. none of these
23. Golu and Mayank start running simultaneously. Golu runs from point A and to point B and Manyank from point B to point A. golu’s speed is 6/5 of Mayank’s speed. After crossing Mayank, if Golu takes 2.5 hr to reach B, how much time does Mayank take to reach A after crossing Golu?
a. 3hr 6min
b. 3hr 16min
c. 3hr 26min
d. 3hr 36min
24. A ball under gravity falls 5 s2m in s seconds. The ball is dropped into a well. The sound of the ball striking the water was heard 59/5 s after it was dropped. Find the depth of the well, if sound travels 324 m/s in air?
25. On a 20km tunnel connection two cities A and B there are three gutters. The distance between gutter 1 and 2 is half the distance between gutter 2 and 3. The distance from city A to its nearest gutter, gutter 1 is equal to the distance of city B from gutter 3. On a particular day the hospital in a city A receives information that an accident has happened at the third gutter. The victim can be saved only if an operation is started within 40 minutes. An ambulance started from city A at 30km/hr and crossed the first gutter after 5 minutes. If the driver had doubled the speed after that, what is the maximum amount of time the doctor would get to attend the patient at the hospital? Assume 1 minute is elapsed for taking the patient into and out of the ambulance.
d. patient died before reaching the hospital
26. Trains are moving from A to B and B to A a regular interval of 1 hr. They complete their journey in 5 hr. How many trains coming from station B will cross the train coming from station that started at 10 am? Assume the trains start from both the stations at the same time.
27. Munna Bhai travels 280 km from Mudhubani to Darbhanga, partly by bus and partly by jeep. Both the vehicles move in the given fashion.
But their maximum speeds differ by 10 km /hr. both the vehicles travel for 6 hr each. Find out their respective maximum speeds. There is no fine gap between movements of both vehicles. (Assume that the bus is moving first and faster than the jeep.)
- 20km/hr, 30km/hr
- 40km/hr, 30km/hr
- 30km/hr, 20km/hr
- 30km/hr, 40km/hr
28. A can complete a piece of work in 4 days. B takes double the time taken by A, C takes double that B, and D takes double that of C to complete the same task. They are paired in groups of two each. One pair takes two thirds the time needed by the second pair to complete the work. Which is the first pair?
29. At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in six hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for this 24 mile round trip, the downstream 12 miles would then take only one hour less than the upstream 12 miles. What is the speed of the current in miles per hour?
30. A tank traveling at 70 kms per hour uses 30% more diesel to travel a certain distance than it does when it travels at the speed of 50 kms per hour. If the truck can travel 19.5 kms on a liter of diesel a 50 kms per hour, how far can the truck travel on 10 litres of diesel at a speed of 70 kms per hour?
31. A tank holds 100 gallons of water. Its inlet is 7 inches in diameter and fills the tank at 5 gallons/min. the outlet of the tank is twice the diameter of the inlet. How many minutes will it take to empty the tank if the inlet is shut off, when the tank is full and the outlet is opened?
32. Among four men P, Q, R, and S, P takes thrice as much time as Q to complete a piece of work. Q takes thrice as much time as R and R takes thrice as much as S to complete the same work. One group of three of the four men can complete the work in 13 days while another group of three can do so in 31 days. Which is the group that takes 13 days?
a. P, Q, S
b. Q, R, S
c. P, R, S
d. P, Q, R
33. In a race, the man who came two places ahead of the last man finished one place ahead of the man who came three places behind the man just ahead of the one who stood second. How many men finished the race?
34. Sujit walks on a plane ground with a constant velocity, turning through a right angle (left or right) after every 20 minutes. If Sujit started at 8.00 am, then which of the following is a possible time at which he can return to his starting point?
35. 2 persons are climbing up on 2 moving escalators, which are also moving up. The ratio of the first person’s speed to that of the first escalator is 4:5 (steps). The ratio of second person’s speed to that of second escalator is 5:7 (steps). If the number of steps visible on each escalator is 180 then the total number of steps taken by both the person to climb up is
36. The velocity of a boat relative to water is 3i+4j and that of the water relative to earth is i+3j. the velocity of the boat relative to the earth is
37. 2 trains T1 and T2 – of equal length are moving in opposite directions. The train T1 overtakes a cyclist C1 moving in the same direction in 30 seconds, while the train T2 crosses the same cyclist C1 in the opposite direction in 20 seconds. If T1 and T2 have equal speeds, in how much time T1 cross T2 completely?
a. 24 seconds
b. 12 seconds
c. 36 seconds
d. 48 seconds
38. A and B start form 2 point P and Q (2000 km apart) respectively with uniform speeds. A is headed towards Q and B towards P. A rests whenever B is on the move and B rests whenever A is on the move. A’s speed is 40 km/hr, while B’s speed is 50 km/hr. A starts first and reaches the destination in 60 hours. Find the least time that B would take to reach his destination after A starts.
d. 75 hours
39. There are three pipes, A B and C opening into a tank. Each pipe can be used to fill or empty the tank at the same respective rate. The ratio of the rates of the three pipes at which they either fill or empty is 2:3:4. Pipes A and B working together, take 3 hours to fill the tank when both are used as inlet pipes. In the first, second and third hours of operation, the pipes, A B and C respectively are used as emptying pipes, while the other two pipes are used as filling pipes. Find the fraction of the tank to be filled at the end of the three hours.
d. none of these
40. A leak E can empty a full tank in 90 minutes. Two filling pipes, P and Q, together, working along with the leak, fill the empty tank in 90 minutes. In how many minutes can P and Q together fill the empty tank, if the leak was completely plugged?
41. Ram and Steve start running simultaneously along a circular track starting from the same point P. If Ram and Steve take 4 minutes and 6 minutes respectively to complete one round along the track, how much time will they take to meet at P for the first time after they start?
42. The population of a city X doubles at the end of every 4 years. What will be population of the city X at the end of 16 years, if its present population is 10000?
43. 2 cars P and Q Start from 2 points A and B towards each other simultaneously. They meet for the first time 40 km from B. after meeting they exchange their speeds as well as directions and proceed to their respective starting points. On reaching their starting points, they turn back with the same speeds and meet at a point 20 km from A. Find the distance between A and B.
For Q! 44 & 45: Answer these questions on the basis of the information given below:
Bhavanipur and Durgapur are 2 small villages which are separated by a distance of 72km. At 6.00am, Aja starts from Bhavanipur and Indu starts from Durgapur, with speeds of f32 km/hr and 16 km/hr respectively and travel towards each other. Every time either of them covers a distance of 8 km their speeds reduce to half of their existing speeds.
44. At what time do they meet?
45. Until the time they meet, for how much time do both of them travel at the same speed?
b. 3.5 hours
c. 4 hours
46. 4 masons A, B, C and D, not necessarily of the same capacity, work in turns, one after the other, each completing exactly one of the four walls of a square compound wall of perimeter 600m. If they took a total of 48 days to finish the work this way, then the length of a wall that all 4 of them working together should be able to complete in a single day is at least
47. A tank can be filled by two taps. The volume of the tank is 5000 liters. Tap I fills the tank at a rate of 1 liters/second. Tap II fills the tank at a rate of 3 liters in 2 seconds. On a particular day, Tap II is opened 100/3 minutes after the time at which Tap I is opened. If after 45 minutes from the time when Tap I was opened, the tank develops a hole which empties the tank at the rate of 2.5 liters/second, how full is the tank in 2 hours from the time when Tap I opened?
48. Thirty poles are located in a straight line such that the distance between any 2 successive poles is 5 meters. A boy stands at a point which is 10 meters away from the first pole, in line with the poles, but not at the third pole. He plays a game. He first runs to the first pole and returns to the starting up point. Then he runs to the second pole and returns to the starting point. What is the distance covered by him in this way by the time he reaches the 30th pole?
d. none of these
49. In 30 days A and B together can do a piece of work that A alone can o in 90 days. After 10 days of the joint work by A and B the scope of the work is increased. The additional work is such that A alone can do it in 30 days. At the same time, because of the increase in the scope of work, C is inducted to speed up things. C alone does the entire work (original +additional) in 20 days. The remaining work can now be finished by A, B and C together in
d. none of these
50. A car P starts from a town A and goes towards point C. At the same time, car Q starts from a town B (lying in between A and C) and goes toward town C. P catches up with Q at a town M between B and C. A car R starts from town C towards town A when the cars P and Q meet. The cars P and R meet at a point N where CN =AB. The cars Q and R meet at a point O where MO =20 km. find AB given AC = 140km and BM =20km