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 Time and Work Questions

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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 : 

Efficiency∝1No 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:

A woman fills a bucket in 6 minutes. 1845 buckets have to be filled from 8 am. to 9:30 am. How many woman employees should be employed for this task?

A) 111 B) 117
C) 123 D) 139
 
Answer & Explanation Answer: C) 123

Explanation:

We know that, M1 × D1W1 = M2 × D2W2

Here M1 = 1, D1 = 6 min, W1 = 1 and M2 = M, D2 = 90 min, W2 = 1845

 

1 × 61 = M × 901845 

=> M = 123

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Q:

It takes one minute to fill 2/7 th of a vessel. What is the time taken in minutes to fill the whole of the vessel  ? 

A) 1/7 min B) 7/2 min
C) 5/7 min D) 7/5 min
 
Answer & Explanation Answer: B) 7/2 min

Explanation:

Time taken to fill 2/7 = 1
Then to fill full 1 = ?
? = 1/(2/7) = 7/2 minutes.

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Q:

A constructor estimates that 4 people can paint Mr. Karthik's house in 6 days. If he uses 5 people instead of 4, how long will they take to complete the job ?

A) 3 days B) 26/3 days
C) 13/4 days D) 24/5 days
 
Answer & Explanation Answer: D) 24/5 days

Explanation:

we know that m1 x d1 = m2 x d2
=> 4 x 6 = 5 x d
where d = no. of days taken by 5 men to paint
d = 24/5 days.

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Q:

Sharan and Mayukh, working together, can complete a task in 18 days. However, Mayukh works alone and leaves after completing 1/3 of the task. Then, Sharan takes over and completees the remaining work by himself. As a result, the duo could complete the task in 40 days. How many days would Sharan alone have taken to do the job if Mayuk' had worked faster than Sharan ?

A) 24 B) 45
C) 72 D) 30
 
Answer & Explanation Answer: B) 45

Explanation:
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Q:

If 10 men take 15 days to complete a work. In how many days will 37 men complete the work?

A) 3 days B) 4 days
C) 5 days D) 6 days
 
Answer & Explanation Answer: B) 4 days

Explanation:

Given 10 men take 15 days to complete a work

=> Total mandays = 15 x 10 = 150

Let the work be 150 mandays.

=> Now 37 men can do 150 mandays in 150/37 =~ 4 days

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Q:

K can lay Highway road between two cities in 16 days. L can do the same job in 12 days. With the help of M, they completes the job in 4 days. How much days does it take for M alone to complete the work ?

A) 47/7 days B) 59/6 days
C) 48/5 days D) 57/5 days
 
Answer & Explanation Answer: C) 48/5 days

Explanation:

Amount of work K can do in 1 day = 1/16

Amount of work L can do in 1 day = 1/12

Amount of work K, L and M can together do in 1 day = 1/4

Amount of work M can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 – 1/12 = 5/48

=> Hence M can do the job on 48/5 days = 9 (3/5) days  

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Q:

Prabhas is twice as good a workman as Rana and finishes a piece of work in 3 hours. In how many hours they together could finish that piece of work?

A) 3 hrs B) 3.5 hrs
C) 2.5 hrs D) 2 hrs
 
Answer & Explanation Answer: D) 2 hrs

Explanation:

Given Prabhas is twice as good a workman as Rana.

Prabhas finishes the work in 3 hrs

=> Rana finishes the work in 6 hrs.

Number of hours required together they could finish the work

= 3 x 6 / 3 + 6

= 18/9

= 2 hrs.

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Q:

Relation Between Efficiencies

6 boys and 8 girls finish a job in 6 days and 14 boys and 10 girls finish the same job in 4 days. In how many days working together 1 boy and 1 girl can finish the work?

Answer

Sol : In this kind of questions we find the work force required to complete the work in 1 day (or given unit of time) then we equate the work force to find the relationship between the efficiencies (or work rate) between the different workers.


 


Therefore, 6B+8G = 6 days


 => 6(6B+8G)= 1 day  (inversely proportional)


 => 36B+48G =1         ( by unitary method)


 


Again  14B+10G = 4days


 => 56B+40G =1


 


so, here it is clear that either we employ 36B and 48G to finish the work in 1 day or 56B and 40G to finish the same job in 1 day. thus , we can say


 => 36B+48G = 56B+40G


 => G= 2.5B


Thus a Girl is 2.5 times as efficient as a boy.


 


Now, since  36B+48G = 1


 => 36B+48(2.5 B)=1


 =>156B=1


i.e., to finish the job in 1 day 156 boys are required or the amount of work is 156 boys-days


 


Again    1G+1B=2.5B+1B=3.5B


 


Now, since 156 boys can finish the job in 1 day


so 1 boy can finish the job in 156 days


Therefore, 3.5 boys can finish the job in 1×1563.5= 47 days.


 


 

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