RRB NTPC Time And Work Questions:

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Question 1: A and B can complete a task in 20 days, B and C can complete it in 30 days while C and A can do the same task together in 24 days. How many days will each of B and C take to complete the task individually?

a) 50 and 54

b) 54 and 72

c) 48 and 80

d) 56 and 64

Question 2: A and B can complete a task in 40 days, B and C can complete it in 30 days while C and A can complete the same task together in 24 days. How many days will each of A, B and C take to complete the task individually?

a) 48, 96 and 32

b) 32, 48 and 96

c) 60, 120 and 40

d) 40, 120 and 60

Question 3: A and B can complete a task together in 35 days. If A works alone and completes 5/7th of the task and then leaves the rest for B to complete by herself, it will take a total of 90 days to complete the task. How many days would it take by A, the more efficient among the duo, to complete the entire work by herself?

a) 40

b) 45

c) 48

d) 42

Question 4: A and B can do a piece of work together in 9 days while A alone can do it in 15 days. They start working together but B leaves 3 days before the completion of the work. For how many days did A and B work together?

a) 7.2

b) 7.5

c) 8.1

d) 8

Question 5: A and B can do a piece of work together in 15 days while A alone can do it in 25 days. They start working together but B leaves 5 days before the completion of the work. For how many days did A and B work together?

a) 10

b) 13

c) 9

d) 12

Question 6: A and B take part in a 100 m race. A runs at 5 km/hr. A gives B a start of 8 m and still beats him by 8 seconds. Find the speed of B.

a) 4.14 km/hr

b) 4.20 km/hr

c) 5.15 km/hr

d) 4.25 km/hr

Question 7: A and B together can complete a task in 12 days. However, if A works alone, completes
half the job and leaves and then B works alone and completes the rest of the work, it takes 25 days in all to complete the work. If B is more efficient than A, how many days would it have taken B to do the work by herself?

a) 18

b) 22

c) 20

d) 15

Question 8: A and can complete a task in 12 days. However, A had to leave a few days before the
task was completed and hence it took 16 days in all to complete the task. If A alone could complete the work in 21 days, how many days before the work getting over did A leave?

a) 7

b) 5

c) 9

d) 3

Question 9: A ball is thrown upward in vacuum at 49 m/sec. The time taken by the ball to reach the highest point is

a) 2.5 Seconds

b) 7.5 Seconds

c) 5 Seconds

d) 15 Seconds

Question 10: A balloon is hovering at a height of 200 m above. A man in a boat on a lake observes it at an elevation of $45^\circ$. 100 seconds later, he sees it at an angle of elevation of $30^\circ$. What is the speed of the boat ?

a) 1.5 m/s

b) 2.2 m/s

c) 2 m/s

d) 1.8 m/s

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Question 11: A clock is set to the right time at 4:00 AM on Thursday. If it gains 20 seconds in every 3 hours, then what is the time shown on the clock at 8:30 PM on Friday night?

a) 8 hours 30 minutes 30 seconds PM

b) 9 hours 34 minutes PM

c) 8 hours 34 minutes PM

d) 8 hours 34 minutes 30 seconds PM

Question 12: A cyclist covers 500 m in 5 minutes. What distance (in km) would the cyclist cover in half an hour if he travels at the same speed ?

a) 3000

b) 3

c) 6

d) 30

Question 13: A cyclist moving on a circular track of radius 100 meters completes one revolution in 2 minutes. What is the approximate speed of the cyclist?

a) 200 m/minute

b) 314 m/minute

c) 300 m/minute

d) 900 m/minute

Question 14: A does a work in 10 days and B does the same work in 15 days. In how many days they together will complete the same work ?

a) 5 days

b) 6 days

c) 8 days

d) 10 days

Question 15: A farmer travelled a distance of 61 km. in a 9 hours. He travelled partly on foot at the rate of 4 km. per hour and partly on bicycle at the rate of 9 km. per hour. The distance travelled on foot is:

a) 17 km.

b) 16 km.

c) 15 km.

d) 14 km.

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Question 16: A flight covering a distance of 1200 kin could reduce the travel time by 30 minutes, due to an additive tailwind that increases the average speed by 120 km/hr. What was the duration of the flight in hours?

a) 2.2 hours

b) 1.9 hours

c) 1.8 hours

d) 2 hours

Question 17: A goods train runs at a speed of 72 km/hr and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?

a) 230 m

b) 240 m

c) 260 m

d) 270 m

Question 18: A hare spots a dog 100 m away and starts running away from it at 12 km/h. One minute later,the dog gives a chase at 16 km/h speed. At what distance from the spot where the hare took flight and the dog catch the hare?

a) 900 m

b) 1000 m

c) 950 m

d) 1100 m

Question 19: A man can row his boat at speed of 4 km/hr and he finds that the time taken rowing upstream is double to that taken downstream. Find the speed of the stream (in km/hr).

a) 1.5

b) 1.3

c) 2

d) 1

Question 20: A man completes a journey in 8 hours. He covers half the distance at 40 km/hr and the rest at 60 km/hr. the length of the journey is :

a) 450 km

b) 420 km

c) 384 km

d) None of the above

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Answers & Solutions:

1) Answer (C)

(A+ B)’s 1 day’s work  = $\frac{1}{20}$

(B + C)’s 1 day’s work = $\frac{1}{30}$

(C + A)’s 1 day’s work = $\frac{1}{24}$

On adding,

2(A + B + C)’s 1 day’s work

= $\frac{1}{20}$ +$\frac{1}{30}$+$\frac{1}{24}$

 
= $\frac{6+4+5}{120}$= $\frac{15}{120}$

∴∴ (A + B + C)’s 1 day’s work

= $\frac{15}{240}$

∴∴ B’s 1 day’s work

=$\frac{15}{240}$ – $\frac{1}{24}$   = $\frac{5}{240}$ = $\frac{1}{48}$

C’s 1 day’s work

= -$\frac{15}{240}$ – $\frac{1}{20}$=
$\frac{3}{240}$ = $\frac{1}{80}$

so, shares = 48 and 80

2) Answer (C)

Total work that can be completed by A and B in one day = $\frac{1}{40}$
Total work that can be completed by A and B in one day = $\frac{1}{30}$
Total work that can be completed by A and B in one day = $\frac{1}{24}$

Total number of days each can complete in one day = $\frac{1}{40} + \frac{1}{30} + \frac{1}{24}$

3) Answer (D)

Fraction of work completed by A is not mentioned.

4) Answer (A)

5) Answer (D)

Let the total work be 75 units.

($\because$ LCM of 15 and 25 is 75.)

Efficiency of A and B = 75/15 = 5

Efficiency of A = 75/25 = 3

B leaves 5 days before the completion of the work so A works 5 days extra so,

5 days work of A = efficiency $\times$ days = 3 $\times$ 5 = 15

Remaining work = 75 – 15 = 60 units

60 units work done by A and B so time taken by together = 60/5 = 12 days

6) Answer (A)

A’s speed$=(5\times\frac{5}{18})m/\sec=\frac{25}{18}m/\sec.$

Time taken by A to cover 100 m $=(100\times\frac{18}{25})\sec=72\sec.$

Time taken by B to cover 92 m = (72 + 8) = 80 sec.

B’s speed $=\frac{92}{80}\times\frac{18}{5}\ kmph=4.14kmph.$

A is correct choice.

7) Answer (C)

Let A took ‘A’ days to complete the task and B took ‘B’ days

then Total time taken = $\frac{AB}{A+B}$=12 ———— Equation (i)

However, A alone taken time = ‘A’ days will be $\frac{A}{2}$ days.

Same for B alone taken time = ‘B’ days will be $\frac{B}{2}$ days.

Total Time = $\frac{A}{2}$ + $\frac{B}{2}$ = 25 days.

A+B= 50 days ——————– Equation (ii)

By (i) and (ii) equation AB = 600 —————– Equation (iii)

A,B =20,30

Because B is more efficient takes less days 80.

A,B,C = 2,8,8

8) Answer (A)

9) Answer (C)

initial velocity=u=49 m/s

final velocity=v=0 m/s

acceleration due to gravity=g=-9.8 $m/s^{2}$

we know, v=u + gt

=>t=-u/t

t=5 s

10) Answer (A)

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11) Answer (D)

12) Answer (B)

Given that a cyclist covers a distance of 500 m in 5 minutes (300 sec) then speed of the cyclist is given by,

s = $\frac{500}{5 \times 60}$

s = $\frac{5}{3}$

Total distance the cyclist would cover in half an hour (1800 sec) if he travels at the same speed is given by,

d = $\frac{5}{3} \times 1800 $ m

d = 3000 m (or) 3km

Hence, option B is the correct answer.

13) Answer (B)

Speed of cyclist = distance covered by cyclist in one round/time taken for one round

distance covered in one round= 2πr= 628 m

thus, speed of cyclist= 628/2= 314 m/minute

14) Answer (B)

Given

A does one work in = 10 days

so in one day A completes $\frac{1}{10}$ work

similarly B does one work in 15 days

so in one day B completes $\frac{1}{15}$ work

so if they work together than the time required by them is

$\frac{1}{10} + \frac{1}{15}$

= $\frac{1}{6}$

hence they complete one work together in 6 days

15) Answer (B)

If t is the time travelled on foot, then 9-t is the time taken on the bicycle.

The distance travelled on foot + the distance travelled on bicycle=total distance travelled

thus, 4t + (9-t)9=61 , distance travelled=Speed x time

On solving we get t=4

So the distance travelled on foot=4×4=16 km

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16) Answer (D)

17) Answer (D)

Trains speed =$72\ \frac{km}{h}=\frac{72000}{3600}=20\ \frac{m}{s}.$

So, in 26 sec , it will cover =$26\times\ 20\ m=520\ m.$

It covers platform’s length and train’s length in 26 secs.

So, Trains length= $\left(520-250\right)=270\ m.$

D is correct choice.

18) Answer (A)

Hare spots a dog at a distance of 100 m

Distance covered by hare in 1 min, $ d =12 km/hr \times \frac{1}{60} $

$ d = \frac{1}{5} km $

= 200 m

Now dog has to cover total 300 m (100 + 200)

Time taken by dog to cover total 300 m ,

Relative speed = 16-12 = 4 km/hr

$ t = \frac{300 m}{4 km/hr} $

300 m = $ \frac{3}{10} km $

Solving , we get $ t= \frac{3}{40} hr $

Distance covered by hare = $ 12 \times \frac{3}{40} $

d = $ \frac{9}{10} km $

= 900 m

19) Answer (B)

20) Answer (C)

Let ‘2d’ be thee total distance covered by the man.

$\dfrac{d}{40}$ + $\dfrac{d}{60}$ = 8

$d = 24*8 = 192$ km

Hence, the total distance covered by the man = 192*2 = 384 km

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