# 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 =$\inline \frac{1}{n}$

2. If A’s 1 day's work =$\inline \frac{1}{n}$, 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 :

$\inline \dpi{100} \fn_jvn Efficiency \propto \frac{1}{number\; of\; time\; units}$

$\inline \dpi{100} \fn_jvn \therefore Efficiency \times time=constant\; work$

Hence, $\inline \dpi{100} \fn_jvn Required \; time = \frac{work}{efficiency}$

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 = $\inline \fn_jvn \frac{100}{efficiency}$

Q:

A and  B can do  a piece of work in 30 days , while  B and C can do the same work in 24 days and C and A in 20 days . They all work together for 10 days when B and C leave. How many days more will A take to finish  the work?

 A) 18 days B) 24 days C) 30 days D) 36 days

Explanation:

2(A+B+C)'s 1 day work = $\inline&space;{\color{Black}\left&space;(&space;\frac{1}{30}+\frac{1}{24}+\frac{1}{20}&space;\right&space;)=\frac{15}{120}=\frac{1}{8}&space;}$

=>(A+B+C)'s  1 day's work=$\inline&space;{\color{Black}\frac{1}{16}&space;}$

work done by A,B and C in 10 days=$\inline&space;{\color{Black}\frac{10}{16}=&space;\frac{5}{8}}$

Remaining work=$\inline&space;{\color{Black}(1-\frac{5}{8})=&space;\frac{3}{8}}$

A's 1 day's work =$\inline&space;{\color{Black}(\frac{1}{16}-\frac{1}{24})=\frac{1}{48}}$

Now, $\inline&space;{\color{Black}\frac{1}{48}}$ work is done by A in 1 day.

So, $\inline&space;{\color{Black}\frac{3}{8}}$ work  wil be done by A in $\inline&space;{\color{Black}(48\times&space;\frac{3}{8})}$ = 18 days

11 7685
Q:

A can do a certain work in the same time in which B and C together can do it.If A and B together could do it in 20 days and C alone in 60 days ,then B alone could do it in:

 A) 20days B) 40 days C) 50 days D) 60 days

Explanation:

(A+B)'s 1 day's work=1/20

C's 1 day work=1/60

(A+B+C)'s 1 day's work=$\inline&space;{\color{Black}&space;\left&space;(&space;\frac{1}{20}&space;+&space;\frac{1}{60}\right&space;)=\frac{4}{60}=\frac{1}{15}}$

Also A's 1 day's work =(B+C)'s 1 day's work

$\inline&space;{\color{Black}&space;\therefore&space;}$ we get: 2 * (A's 1 day 's work)=1/15

=>A's 1 day's work=1/30

$\inline&space;{\color{Black}&space;\therefore&space;}$ B's 1 day's work= $\inline&space;{\color{Black}&space;\left&space;(&space;\frac{1}{20}&space;-\frac{1}{30}\right&space;)=\frac{1}{60}}$

So, B alone could do the work in 60 days.

21 7475
Q:

A works twice as fast as B.If  B can complete a work in 18 days independently,the number of days  in which A and B can together finish the work is:

 A) 4 days B) 6 days C) 8 days D) 10 days

Explanation:

Ratio of rates of working of A and B =2:1. So, ratio of times taken =1:2

$\inline&space;{\color{Black}\therefore&space;}$A's 1 day's work=1/9

B's 1 day's work=1/18

(A+B)'s 1 day's work=$\inline&space;{\color{Black}(\frac{1}{9}&space;+\frac{1}{18})=\frac{3}{18}=\frac{1}{6}&space;}$

so, A and B together can finish the work in 6 days

11 5582
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

5543
Q:

A Contractor employed a certain number of workers  to finish constructing a road in a certain scheduled time. Sometime later, when a part of work had been completed, he realised that the work would get delayed by three-fourth of the  scheduled time, so he at once doubled the no of workers and thus he managed to finish the road on the scheduled time. How much work he had been completed, before increasing the number of workers?

 A) 10 % B) 14 2/7 % C) 20 % D) Can't be determined

Explanation:

Let he initially employed x workers which works for D days and he estimated 100 days for the whole work and then he doubled the worker for (100-D) days.

D * x +(100- D) * 2x= 175x

=>  D= 25 days

Now , the work done in 25 days = 25x

Total work = 175x

therefore, workdone before increasing the no of workers = $\frac{25x}{175x}\times&space;100=14\frac{2}{7}$ %