8
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:   D) 8 hrs 34 min

Explanation:

Number of pages typed by Adam in 1 hour = $\inline \fn_jvn \small \frac{36}{6}$ = 6
Number of pages typed by Smith in 1 hour = $\inline \fn_jvn \small \frac{40}{5}$ = 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 $\inline \fn_jvn \small \frac{4}{7}$ = 8 hrs 34 min.

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

Sol :  Number of persons $\inline&space;\fn_jvn&space;\times$ days = work

20 $\inline&space;\fn_jvn&space;\times$ 7 = 140 man- days

Now,  $\inline&space;\fn_jvn&space;x\times$ 28  = 140 man- days

$\inline&space;\fn_jvn&space;\Rightarrow&space;x=5$

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

Second method:

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

$\inline&space;\fn_jvn&space;20\times&space;7=M_{2}\times&space;28$

$\inline&space;\fn_jvn&space;\Rightarrow&space;M_{2}=5$

352
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?

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

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

Net efficiency = 5-1.66 = 3.33%

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

290
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?

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

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

but    2x-x=30

$\inline&space;\fn_jvn&space;\Rightarrow$  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%

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

Note:      Efficiency $\inline&space;\fn_jvn&space;\prec$ $\inline&space;\fn_jvn&space;\frac{1}{number\:&space;of&space;\:&space;time\:&space;units}$

$\inline&space;\fn_jvn&space;\therefore$ Efficiency $\inline&space;\fn_jvn&space;\times$  time = Constant Work

Hence, Required time = $\inline&space;\fn_jvn&space;\frac{work}{efficiency}$

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

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

6048
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?

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

B's i days work =$\inline&space;\fn_jvn&space;\frac{1}{6}$

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

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

Alternatively :

Efficiency of A =$\inline&space;\fn_jvn&space;\frac{100}{12}$ =8.33%

Efficiency of B =$\inline&space;\fn_jvn&space;\frac{100}{6}$ =16.66%

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

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

307
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

Explanation:

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

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

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

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

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

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

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