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:

P and Q can do a work in 4 hours and 12 hours respectively. P starts the work at 9am and they work alternately for one hour each. When will the work be completed ?

A) 3 am B) 12 pm
C) 1 pm D) 3 pm
 
Answer & Explanation Answer: D) 3 pm

Explanation:

Work done by P and Q in the first two hours, working alternately
= First hour P + Second hour Q
  work is completed in 2 hours
Then, the total time required to complete the work by P and Q working alternately=23=6hours
Thus, work will be completed at 3pm.

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Q:

After working for 8 days, Arun finds that only  rd of the work has been done. He employs Akhil who is 60% as efficient as Arun. How many days more would Akhil take to complete the work?

A) 24.5 days B) 26.6 days
C) 25 days D) 20 days
 
Answer & Explanation Answer: B) 26.6 days

Explanation:

Arun has completed  rd of the work in 8 days
Then he can complete the total work in
 ---- 8
1 ---- ?
= 24 days
But given Akhil is only 60% as efficient as Arun
Akhil = 
Akhil can complete the total work in 40 days
Now, remaining 2/3rd of work can be completed in
1 ------   40
  ------   ?    26.66 days.

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Q:

50 men can build a tank in 40days, but though they begin the work together, 5 men quit every ten days. The time needed to build the tank is ?

A) 50 days B) 48 days
C) 47.5 days D) 49 days
 
Answer & Explanation Answer: A) 50 days

Explanation:

50 men can build a tank in 40 days
Assume 1 man does 1 unit of work in 1 day
Then the total work is 50×40 = 2000 units

50 men work in the first 10 days and completes 50×10 = 500 units of work
45 men work in the next 10 days and completes 45×10 = 450 units of work
40 men work in the next 10 days and completes 40×10 = 400 units of work
35 men work in the next 10 days and completes 35×10 = 350 units of work
So far 500 + 450 + 400 + 350 = 1700 units of work is completed and

remaining work is 2000 - 1700 = 300 units

30 men work in the next 10 days. In each day, they does 30 units of work.

Therefore, additional days required = 

Thus, total 10+10+10+10+10 = 50 days required.

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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


       \inline \fn_jvn \Rightarrow 6(6B+8G)= 1 day  (inversely proportional)


       \inline \fn_jvn \Rightarrow 36B+48G =1         ( by unitary method)


       Again  14B+10G = 4days


       \inline \fn_jvn \Rightarrow 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


        \inline \fn_jvn \Rightarrow    36B+48G = 56B+40G


        \inline \fn_jvn \Rightarrow    20B = 8G


        \inline \fn_jvn \Rightarrow     G= 2.5B


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


Now, since        36B+48G = 1


        \inline \fn_jvn \Rightarrow 36B+48 \inline \fn_jvn \times (2.5 B)=1


        \inline \fn_jvn \Rightarrow                   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 1 \inline \fn_jvn \times 156 days


\inline \fn_jvn \therefore 3.5 boys can finish the job in \inline \fn_jvn \frac{1\times 156}{3.5} = \inline \fn_jvn 44\frac{4}{7} days.


 

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Q:

K can build a wall in 30 days. L can demolish that wall in 60 days. If K and L work on alternate days, when will the wall be completed ?

A) 120 days B) 119 days
C) 118 days D) 117 days
 
Answer & Explanation Answer: D) 117 days

Explanation:

K's work in a day(1st day) = 1/30
L's work in a day(2nd day)= -1/60(demolishing)
hence in 2 days, combined work= 1/30 - 1/60
=1/60
since both works alternatively, K will work in odd days and L will work in even days.
1/60 unit work is done in 2 days
58/60 unit work will be done in 2 x 58 days = 116 days
Remaining work = 1-58/60
= 2/60
= 1/30
Next day, it will be K's turn and K will finish the remaining 1/30 work.
hence total days = 116 + 1 = 117.

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