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:

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.

{\color{Black} \therefore } 1 woman's  1 day's work =\inline {\color{Black} \frac{1}{60} }

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

\inline {\color{Black}\therefore } 1 man's  1 day's work =\inline {\color{Black}\frac{1}{30} }

so, required ratio =\inline {\color{Black}\frac{1}{30} } :\inline {\color{Black}\frac{1}{60} } = 2:1

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3 1027
Q:

Adam and Smith are working on a project. Adam takes 6 hrs to type 36 pages on a computer, while Smith takes 5 hrs to type 40 pages. How much time will they take, working together on two different computers to type a project of 120 pages?

A) 8 hrs 45 min B) 8 hrs 42 min
C) 8 hrs D) 8 hrs 34 min
 
Answer & Explanation Answer: D) 8 hrs 34 min

Explanation:

Number of pages typed by Adam in 1 hour =  = 6
Number of pages typed by Smith in 1 hour =  = 8
Number of pages typed by both in 1 hour = (6 + 8) = 14
Time taken by both to type 110 pages = (120 * 1/14) = 8  = 8 hrs 34 min.

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9 1002
Q:

A and B together finish a wor in 20 days.They worked together for 15 days and then B left. Afer another 10 days,A finished the remaining work. In how many days A alone  can finish the job?

A) 30 B) 40
C) 50 D) 60
 
Answer & Explanation Answer: B) 40

Explanation:

(A+B)'s 15 days work=\inline {\color{Blue} (\frac{1}{20}\times 15)=\frac{3}{4}}

Remaining work =\inline {\color{Blue} (1-\frac{3}{4})=\frac{1}{4}}

Now, \inline {\color{Blue} \frac{1}{4}} work is done by A in 10 days.

Whole work will bedone by A in \inline {\color{Blue} (10\times 4)=40} days.

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2 997
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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7 991
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

Sol :  Number of persons \inline \fn_jvn \times days = work 


                 20 \inline \fn_jvn \times 7 = 140 man- days


         Now,  \inline \fn_jvn x\times 28  = 140 man- days


         \inline \fn_jvn \Rightarrow x=5


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


 


Second method:


          Since work is constant, therefore  \inline \fn_jvn M_{1}\times D_{1}= M_{2}\times D_{2} = Work done


                             \inline \fn_jvn 20\times 7=M_{2}\times 28


                             \inline \fn_jvn \Rightarrow M_{2}=5


 

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