7
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:

A contractor undertakes to complete a work in 130 days. He employs 150 men for 25 days and they complete 1/4 of the work . He then reduces the number of men to 100, who work for 60 days, after which there are 10 days holidays.How many men must be employed for the remaining period to finish the work?

150 men in 25 days do = $\inline \frac{1}{4}$ work

1 man in 1 day does = $\inline \frac{1}{4}\times \frac{1}{25}\times \frac{1}{150}$ work

$\inline \therefore$ 100 men in 60 days do = $\inline \frac{1}{4}\times \frac{1}{25}\times \frac{1}{150}\times 100\times 60=\frac{2}{5}$ work

Total work done =$\inline \frac{1}{4}+\frac{2}{5}=\frac{5+8}{20}=\frac{13}{20}$

$\inline \therefore$ Remaining work =$\inline 1-\frac{13}{20}=\frac{7}{20}$

Remaining time = 130 - (25+60+10) = 35 days

$\inline \therefore\: \frac{1}{4}$work is done in 25 days  by 150 men

$\inline \therefore\: \frac{7}{20}$ work is done in 35 days by $\inline \frac{150\times 4\times 25\times 7}{35\times 20}=150$ men

1258
Q:

A can do a piece of work in 18 days, B in 27 days, C in 36 days. They start worked together . But only C work till the completion of work. A leaves 4 days and B leaves 6 days before the completion of work. In how many days work be completed?

Let the work be completed in x days

(x-4)days of A + (x-6)days of B + x days of C = 1

$\inline&space;\Rightarrow$ $\inline&space;\frac{x-4}{18}+\frac{x-6}{27}+\frac{x}{36}=1$

$\inline&space;\Rightarrow&space;\frac{13x-48}{108}=1$

x = 12

$\inline&space;\therefore$ Total time = 12 days

2084
Q:

A and B can do a piece of work in 40 and 50 days. If they work at it an alternate days with A beginning in how many days, the work will be finished ?

(A+B)'s two days work = $\inline&space;\frac{1}{40}+\frac{1}{50}=\frac{9}{200}$

Evidently, the work done by A and B duing 22 pairs of days

i.e in 44 days = $\inline&space;22\times&space;\frac{9}{200}=\frac{198}{200}$

Remaining work = $\inline&space;1-\frac{198}{200}=\frac{1}{100}$

Now on 45th day A will have the turn to do $\inline&space;\frac{1}{200}$ of the work and this work A will do in $\inline&space;40\times&space;\frac{1}{100}-\frac{2}{3}$

$\inline&space;\therefore$ Total time taken = $\inline&space;44\frac{2}{5}$ daya

694
Q:

P and Q undertake to do a piece of work for Rs. 400. One alone can do it in 6 days , the other in 8 days. With the help of a boy , they finish it in 3 days . Find the boy's share?

P's 1 day's work = $\inline&space;\frac{1}{6}$;      Q's 1 day's work = $\inline&space;\frac{1}{8}$

Boy's one day's work = $\inline&space;\frac{1}{3}-(\frac{1}{6}+\frac{1}{8})=\frac{1}{24}$

Ratio of their shares = $\inline&space;\frac{1}{6}:\frac{1}{8}:\frac{1}{24}=4:3:1$

$\inline&space;\therefore$ Boy's share = $\inline&space;400\times&space;\frac{1}{8}$ = 50/-

301
Q:

A contractor  undertook a project to complete it in 20 days which needed 5 workers to work continuously for all the days estimated. But before the start of the work the client wanted to complete it earlier than the scheduled time, so the contractor calculated that  he needed to increase 5 additional  men every 2 days to complete the work in the time the client wanted it:

If the work was further increased by 50% but the contractor continues to increase the 5 workers o every 2 days then how many more days are required over the initial time specified by the  client.

 A) 1 day B) 2 days C) 5 days D) None of these