# Time and Work Questions

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

35 8950
Q:

A can do a piece of work in 10 days, B in 15 days. They work together for 5 days, the rest of the work is finished by C in two more days. If they get Rs. 3000 as wages for the whole work, what are the daily wages of A, B and C respectively (in Rs):

 A) 200, 250, 300 B) 300, 200, 250 C) 200, 300, 400 D) None of these

Explanation:

A's 5 days work = 50%

B's 5 days work = 33.33%

C's 2 days work = 16.66%          [100- (50+33.33)]

Ratio of contribution of work of A, B and C = $\inline \fn_jvn 50:33\frac{1}{3}:16\frac{2}{3}$

= 3 : 2 : 1

A's total share = Rs. 1500

B's total share = Rs. 1000

C's total share = Rs. 500

A's one day's earning = Rs.300

B's one day's earning = Rs.200

C's one day's earning = Rs.250

34 12738
Q:

A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?

 A) 11 days B) 12 days C) 13 days D) 14 days

Explanation:

One day's work of A, B and C = (1/24 + 1/30 + 1/40) = 1/10

C leaves 4 days before completion of the work, which means only A and B work during the last 4 days.

Work done by A and B together in the last 4 days = 4 (1/24 + 1/30) = 3/10

Remaining Work = 7/10, which was done by A,B and C in the initial number of days.

Number of days required for this initial work = 7 days.

Thus, the total numbers of days required = 4 + 7 = 11 days.

24 7768
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 = $\frac{25x}{175x}\times&space;100=14\frac{2}{7}$ %

17 2680
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 = $\inline&space;\fn_jvn&space;\frac{100}{efficiency}$