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 =1n

2. If A’s 1 day's work =1n, 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 : 

Efficiency1No of time units

 

 Efficiency × Time = Constant Work

 

Hence, Required time = WorkEfficiency

 

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 = 100Efficiency

Q:

P and Q can complete a job in 24 days working together. P alone can complete it in 32 days. Both of them worked together for 8 days and then P left. The number of days Q will take to complete the remaining work is ?

A) 56 days B) 54 days
C) 60 days D) 64 days
 
Answer & Explanation Answer: D) 64 days

Explanation:

(P+Q)'s 1 day work = 1/24

P's 1 day work = 1/32

=> Q's 1 day work = 1/24 - 1/32 = 1/96

Work done by (P+Q) in 8 days = 8/24 = 1/3

Remainining work = 1 - 1/3 = 2/3

Time taken by Q to complete the remaining work = 2/3 x 96 = 64 days.

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22 15989
Q:

4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it ?

A) 40 days B) 36 days
C) 32 days D) 34 days
 
Answer & Explanation Answer: A) 40 days

Explanation:

Let 1 man's 1 day work = x and 1 woman's 1 day work = y.
Then, 4x + 6y = 1/8 and 3x + 7y = 1/10
Solving these two equations, we get:
x = 11/400 and y = 1/400
10 woman's 1 day work = (1/400 x 10) = 1/40.

Hence, 10 women will complete the work in 40 days.

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19 15781
Q:

If 2 men and 3 women can do a piece of work in 8 days and 3 men and 2 women in 7 days. In how many days can the work be done by 5 men and 4 women working together?

A) 3 days B) 6 days
C) 4 days D) 2 days
 
Answer & Explanation Answer: C) 4 days

Explanation:

From the given data,

=> (2 M + 3W) 8 = (3M + 2W)7

=> 16M + 24W = 21M + 14 W

=> 10W = 5M

=> 2W = M

=> 14W × ? = 7W × 8

? = 4 days

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29 15501
Q:

Two pipes A and B can fill a tank in 24 hours and 1717 hours respectively. Harihar opened the pipes A and B to fill an empty tank and some times later he closed the taps A and B , when the tank was supposed to be full. After that it was found that the tank was emptied in 2.5 hours because an outlet pipe "C" connected to the tank was open from the beginning. If Harihar closed the pipe C instead of closing pipes A and B the remaining tank would have been filled in :

A) 2 hours B) 8 hours
C) 6 hours D) 4 hours
 
Answer & Explanation Answer: B) 8 hours

Explanation:

Efficiency of Inlet pipe A = 4.16%       10024 

 

Efficiency of Inlet pipe B = 5.83%      1001717  

 

Therefore, Efficiency of A and B together = 100 %   

 

Now, if the efficiency of outlet pipe be x% then in 10 hours the capacity of tank which will be filled = 10 *  (10 - x)

 

Now, since this amount of water is being emptied by 'C' at x% per hour, then

 

 10x10-xx=2.5 hrs 

 => x = 8 

 

Therefore, in 10 hours 20% tank is filled only. Hence, the remaining 80% of the  capacity will be filled by pipes A and B  in 80/10 = 8 hours 

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38 14839
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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20 14674
Q:

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

A) 16 days B) 13 days
C) 15 days D) 12 days
 
Answer & Explanation Answer: B) 13 days

Explanation:

Ratio of times taken by P & Q = 100 : 130 = 10:13

 

Let Q takes x days to do the work

Then, 10:13 :: 23:x

=> x = 23x13/10

=> x = 299/10

 

P's 1 day's work = 1/23

Q's 1 day's work = 10/299

(P+Q)'s 1 day's work = (1/23 + 10/299) = 23/299 = 1/13

Hence, P & Q together can complete the work in 13 days.

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17 14541
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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30 13680
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 = 56Remaining 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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28 13153