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:   D) 8 hrs 34 min


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.


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


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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2 352

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?


Sol : Filling efficiency = 5%               \inline \fn_jvn \left ( \because 5=\frac{100}{20} \right )

       emptying efficiency = 1.66%      \inline \fn_jvn \left ( \because 1.66=\frac{100}{60} \right )

       Net efficiency = 5-1.66 = 3.33%

       \inline \fn_jvn \therefore Required time to fil the tub =\inline \fn_jvn \frac{100}{3.33} = 30 minutes


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1 290

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?


Sol:       Ratio of efficiency = 2:1 (A:B)

       Ratio of required time = 1:2 (A:B)       \inline \fn_jvn \Rightarrow x:2x

       but    2x-x=30  

       \inline \fn_jvn \Rightarrow  x= 30  and  2x= 60

       Now   efficiency of A =3.33%  and efficiency of B =1.66%

       Combined efficiency of A and B together = 5%

       \inline \fn_jvn \therefore time required by A and B working together to finish the work = \inline \fn_jvn \frac{100}{5} = 20 days



Note:      Efficiency \inline \fn_jvn \prec \inline \fn_jvn \frac{1}{number\: of \: time\: units}

             \inline \fn_jvn \therefore Efficiency \inline \fn_jvn \times  time = Constant Work

             Hence, Required time = \inline \fn_jvn \frac{work}{efficiency}

whole work is always cosidered as 1, in terms of fraction and 100%, in terms of percentage.

In, general no.of days or hours = \inline \fn_jvn \frac{100}{efficiency}      

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12 6048

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?


Sol : A's i days work = \inline \fn_jvn \frac{1}{12}

        B's i days work =\inline \fn_jvn \frac{1}{6}

       \inline \fn_jvn \therefore (A+B)'s 1 day's work= \inline \fn_jvn \frac{1}{12}+\frac{1}{6}=\frac{3}{12}=\frac{1}{4}

       \inline \fn_jvn \therefore Time taken by both to finish the whole work = \inline \fn_jvn \frac{1}{\frac{1}{4}} = 4 days


Alternatively :

      Efficiency of A =\inline \fn_jvn \frac{100}{12} =8.33%

      Efficiency of B =\inline \fn_jvn \frac{100}{6} =16.66%

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

\inline \fn_jvn \therefore Time taken by both to finish the work (working together) =\inline \fn_jvn \frac{100}{25} = 4days

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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


1 man's 1 day work =\inline {\color{Black}\frac{1}{96} } ; 1 woman's 1 day work =\inline {\color{Black}\frac{1}{192} }

work done in 6 days= \inline {\color{Black}6(\frac{8}{96}+\frac{8}{192}) =(6\times \frac{1}{8})=\frac{3}{4}}

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

(8 men +8 women)'s 1 day work =\inline {\color{Black}1(\frac{8}{96}+\frac{8}{192})}=\inline {\color{Black}\frac{1}{8}}

Remaining work=\inline {\color{Black}(\frac{1}{4}-\frac{1}{8})=\frac{1}{8}}

\inline {\color{Black}\frac{1}{96}} work is done in 1 day by 1 man

\inline {\color{Black}\therefore }\inline {\color{Black}\frac{1}{8}} work will be done in 1 day by \inline {\color{Black}(96\times \frac{1}{8})=12} men

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