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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:

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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Subject: Time and Work

2 3454
Q:

Application of Inverse Proportion

If 20 persons can do a piece of work in 7 days then calculate the number of persons require to complete the work in 28 days

Answer

Number of persons * days = work  


20 * 7 = 140 man- days 


 


Now,  x * 28  = 140 men- days


=> x =5         


Therefore in second case the required number of person is 5.


 


Second method:


Since work is constant, therefore  M1 x D1= M2 x D2


20 x 7 = M2 x 28


=> M2 = 5 


 

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Subject: Time and Work

5 4767
Q:

Concept of Nehative Work

A tub can be filed in 20 minutes but there is a lekage in it which can empty the full tub in 60 minutes. In how many minutes it can be filled?

Answer

Filling efficiency = 5%        


Emptying efficiency = 1.66%  


Net efficiency = 5-1.66 = 3.33%


Therefore, Required time to fil the tub =100/3.33= 30 minutes

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Subject: Time and Work

2 2367
Q:

Relation Between Efficiency and Time

A is twice as good a workman as B and is therefore able to finish a piece of work in 30 days less than B.In how many days they can complee the whole work; working together?

Answer

Ratio of times taken by A and B = 1 : 2.


The time difference is (2 - 1) 1 day while B take 2 days and A takes 1 day.


If difference of time is 1 day, B takes 2 days.


If difference of time is 30 days, B takes 2 x 30 = 60 days.


So, A takes 30 days to do the work.


 


A's 1 day's work = 1/30


B's 1 day's work = 1/60


(A + B)'s 1 day's work = 1/30 + 1/60 = 1/20


A and B together can do the work in 20 days.

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Subject: Time and Work

249 62529
Q:

Concept of Efficiency

A can do a job in 12 days and B can do the same job in 6 days, in how many days working together they can complete the job?

Answer

A's 1 days work = 1/12 


B's 1 days work =1/6


Therefore, (A+B)'s 1 day's work= 1/12 + 1/6 = 1/4       


Therefore, Time taken by both to finish the whole work = 114 = 4 days


 


Alternatively :


Efficiency of A =100/12 =8.33%


Efficiency of B =100/6=16.66%


Combined efficiency of A and B both = 8.33+16.66=25%


Therefore, Time taken by both to finish the work (working together) =100/25= 4days

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Subject: Time and Work

3 5465
Q:

12 men can complete a work in 8 days. 16 women can complete the same work in 12 days. 8 men and 8 women started working  and worked for 6 days. How many more men are to be added to complete the remaining work in 1 day?

A) 8 B) 12
C) 16 D) 24
 
Answer & Explanation Answer: B) 12

Explanation:

1 man's 1 day work =1/96 ; 1 woman's 1 day work = 1/192

Work done in 6 days=6896+8192=6×18 =34 

Remaining work = 1/4

(8 men +8 women)'s 1 day work = 1896+8192 =1/8

Remaining work =1/4 -  1/8 = 1/8

 

 1/96 work is done in 1 day by 1 man

 

Therefore, 1/8 work will be done in 1 day by 96 x (1/8) =12 men

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Filed Under: Time and Work

309 66426
Q:

Ten women can do a work in six days. Six men can complete the same work in five days. What is the ratio between the capacity of a man and a woman?

A) 1:2 B) 2:1
C) 2:3 D) 3:2
 
Answer & Explanation Answer: B) 2:1

Explanation:

(10 * 6) women can complete the work in 1 day.

 Therefore, 1 woman's  1 day's work = 1/60

 

(6 * 5) men can complete the work in 1 day.

 Therefore, 1 man's  1 day's work = 1/30

 

so, required ratio =1/30 : 1/60 = 2:1

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Filed Under: Time and Work

4 7150
Q:

A and B together can do a piece of work in 40 days. A having worked for 20 days, B finishes the remaining work alone in 60 days. In How many days shall B finish the  whole work alone?

A) 60 B) 70
C) 80 D) 90
 
Answer & Explanation Answer: C) 80

Explanation:

Let A's 1 day's work=x and B's 1 day's work=y

Then x+y = 1/40 and 20x+60y=1 

Solving these two equations , we get : x= 1/80 and y= 1/80

Therefore B's  1 day work = 1/80

Hence,B alone shall finish the whole work in 80 days

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Filed Under: Time and Work

31 23482