Time and Work Questions

FACTS  AND  FORMULAE  FOR  TIME  AND  WORK  QUESTIONS

 

 

1. If A can do a piece of work in n days, then A's 1 day's work =

2. If A’s 1 day's work =, then A can finish the work in n days.

 

3. A is thrice as good a workman as B, then:

Ratio of work done by A and B = 3 : 1.

Ratio of times taken by A and B to finish a work = 1 : 3.

 

NOTE : 

Hence, 

 

Whole work is always considered as 1, in terms of fraction and 100% , in terms of percentage.

In general, number of day's or hours = 

Q:

Two pipes A and B can fill a cistern in 4 minutes and 6 minutes respectively . If these pipes are turned on alternately for 1 minute each how long will it take to the cistern to fill?

Answer

As the pipes are operating alternatively, thus their 2 minutes job is = 14 + 16 = 512


 


In the next 2 minutes the pipes can fill another 512 part of cistern.


 


Therefore, In 4 minutes the two pipes which are operating alternatively will fill 


512 + 512 = 56


 


Remaining part = 1 - 56 = 16


 


Pipe A can fill 14 of the cistern in 1 minute


 


Pipe A can fill 16 of the cistern in = 23 min


 


 


 


Therefore, Total time taken to fill the Cistern 


 


4 + 23 minutes.

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8 4014
Q:

A is twice efficient as B and together they do the same work in as much time as C and D together. If C and D can complete the work in 20 and 30 daysrespectively, working alone ,then in how many days A can complete the work individually:

A) 12 days B) 18 days
C) 24 days D) 30 days
 
Answer & Explanation Answer: B) 18 days

Explanation:

                                              A     +      B        =      C     +     D

                                              |              |                 |             |

    Ratio of efficiency         10x   +    5x               9x     +   6x

                                            |________|                 |_________|  

                                                 15x                           15x

Therefore , ratio of efficiency of A:C  =10:9

Therefore,  ratio of days taken by A:C = 9:10

Therefore, number of days taken by A = 18 days                 

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6 3911
Q:

Four pipes P,Q, R and S can fill a cistern in 20,25, 40 and 50 hours respectively.The first pipe P was opened at 6:00 am, Q at 8:00 am, R at 9:00 am and S at 10:00 am. when will the Cistern be full?

A) 4:18 pm B) 3:09 pm
C) 12:15 pm D) 11:09 am
 
Answer & Explanation Answer: B) 3:09 pm

Explanation:

Efficiency of P= 100/20= 5% per hour

Efficiency of Q= 100/25= 4% per hour

Efficiency of R= 100/40= 2.5% per hour

Efficiency of S=100/50= 2% per hour

 

Cistern filled till 10 am by P, Q and R

Till 10.00am Pipe P filled 20%Till 10.00am Pipe Q filled 8%Till 10.00am Pipe R filled 2.5%30.5%

 

Thus, at 10 am pipe P,Q and R filled 30.5% of the cistern.

Rest of cistern to be filled = 100 - 30.5 = 69.5%

Now, the time taken by P,Q,R and S together to fill the remaining capacity of the cistern

  =69.5 / (5+4+2.5+2) = 5 Hours and 9 minutes(approx)

 

Therefore, total time =4 hrs + 5hrs 9 mins 

                              = 9 hrs and 9 mins

 

It means cistern will be filled up at 3:09 pm

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5 3466
Q:

When A, B and C are deployed for a task , A and B together do 70% of the work and B and C together do 50% of the work. who is most efficient?

A) A B) B
C) C D) can't be determined
 
Answer & Explanation Answer: A) A

Explanation:

A + B= 70%             

B + C =50%  

  (A+B)+(B+C)-(A+B+C)= B

=> B= 20%     A= 50%        and   C=30%

 Hence A is most efficient

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9 3439
Q:

A and B can do a piece of work in 40 and 50 days. If they work at it an alternate days with A beginning in how many days, the work will be finished ?

Answer

(A+B)'s two days work = 140+150=9200 


 


Evidently, the work done by A and B duing 22 pairs of days 


 


 i.e in 44 days = 22×9200=198200 


 


Remaining work = 1-198200= 1/100


 


 Now on 45th day A will have the turn to do 1/100 of the work and this work A will do in 40×1100=25


 


 Therefore,  Total time taken = 4425daya

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2 3352
Q:

A tank has an inlet and outlet pipe. The inlet pipe fills the tank completely in 2 hours when the outlet pipe is plugged. The outlet pipe empties the tank completely in 6 hours when the inlet pipe is pluggeed.

If there is a lekage also which is capable of draining out the liquid from the tank at half of the  rate of outet pipe,them what is the time taken to fill the emty tank when both the pipes are opened?

A) 3 hours B) 4 hours
C) 5 hours D) None of these
 
Answer & Explanation Answer: B) 4 hours

Explanation:

Rate of leakage = 8.33% per hour

Net efficiency = 50 - (16.66 + 8.33)= 25%

Time required = 100/25 = 4 hours

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7 3129
Q:

Amit can do a piece of work in 45 days, but Bharath can do the same work in 5 days less, than Amit, when  working alone. Amit and Bharath both started the work together but Bharath  left after some days and Amit finished the remaining work in 56 days with half of his efficiency but he did the work with Bharath with his complete efficiency. For how many days they had worked together?

A) 6 B) 8
C) 9 D) 12
 
Answer & Explanation Answer: B) 8

Explanation:

    AmitBharatNo.of Days4540Efficiency2.22Percent(=145)2.5 Percent(=140)

 

Amit did the work in 56 days = 56×145×2=2845 

 

Therefore, Rest work 17/45 was done by Amit and Bharath = 174517360 = 8 days

 

 

 

( since Amit and Bharath  do the work in one day = 145+140=17360)

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7 2957
Q:

A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days  ?

A) 9 days B) 11 days
C) 13 days D) 15 days
 
Answer & Explanation Answer: C) 13 days

Explanation:

Ratio of times taken by A and B = 100 : 130 = 10 : 13.
Suppose B takes x days to do the work.

Then, 10 : 13 :: 23 : x     =>     x = ( 23 x 13/10 )     =>     x = 299 /10.

A's 1 day's work = 1/23 ;
B's 1 day's work = 10/299 .

(A + B)'s 1 day's work = ( 1/23 + 10/299 ) = 23/299 = 113 .

Therefore, A and B together can complete the work in 13 days. 

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9 2659