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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

a.
35

b.
15

c.
29

d.
31

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

a.
700km

b.
420km

c.
525km

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?

a.
Rs.14.

b.
Rs.5

c.
Rs.20

d.
Rs.7

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?

a.
3

b.
4

c.
5

d.
6

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

c.
27miles

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?

a.
3:1

b.
4:1

c.
5:1

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

b.
7pm

c.
7.20 pm

d.
8pm

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?

a.
200km

b.
400km

c.
450km

d.
500km

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 – 3

^{rd}the time. How many workers were there in the group?
a.
2

b.
3

c.
5

d.
10

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.

a.
50km

b.
50√2km

c.
25km

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 4

^{th}, 7^{th}, 9^{th}and 13^{th}minutes, how far will he be from the starting point at the end of the 10 minute?
a.
2/15km

b.
3/15km

c.
4/15km

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

a.
65m/s

b.
65km/hr

c.
56m/s

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?

a.
125m

b.
180m

c.
245m

d.
30m

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.

a.
4minute

b.
2.5minute

c.
1.5minutes

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.

a.
10

b.
11

c.
12

d.
13

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?

a.
A,B

b.
A,C

c.
B,C

d.
A,D

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?

a.
7/3

b.
4/3

c.
5/3

d.
8/3

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?

a.
130

b.
140

c.
150

d.
175

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?

a.
7.14min

b.
10.0min

c.
0.7min

d.
5.0min

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?

a.
4

b.
5

c.
6

d.
7

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?

a.
11.20am

b.
12.40pm

c.
1.00pm

d.
2.40pm

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

a.
140

b.
145

c.
155

d.
165

e.

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.

a.
100hours

b.
90hours

c.
80hours

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.

a.
1/5

b.
2/5

c.
3/5

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?

a.
45min

b.
180min

c.
60min

d.
90min

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?

a.
4min

b.
6min

c.
10min

d.
12min

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?

a.
50000

b.
80000

c.
160000

d.
320000

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.

a.
130km

b.
100km

c.
120km

d.
110km

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?

a.
1.30pm

b.
1.35pm

c.
1.40pm

d.
1.45pm

45. Until the
time they meet, for how much time do both of them travel at the same speed?

a.
1hour

b.
3.5 hours

c.
4 hours

d.
6.5hours

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

a.
33.33m

b.
50m

c.
66.66m

d.
87.5m

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?

a.
1/10

b.
full

c.
3/5

d.
4218/5000

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 30

^{th}pole?
a.
4785m

b.
4795m

c.
4800m

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

a.
20days

b.
10days

c.
25days

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

- 40km
- 30km
- 20km
- 50km

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