# 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 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

81 29424
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 = $\inline&space;\fn_jvn&space;\frac{100}{efficiency}$

20980
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

58 19674
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.

39 18666
Q:

P can complete a work in 12 days working 8 hours a day.Q can complete the same work in 8 days working 10 hours a day. If both p and Q work together,working 8 hours a day,in how many days can they complete the work?

 A) 60/11 B) 61/11 C) 71/11 D) 72/11

Explanation:

P can complete the work in (12 * 8) hrs = 96 hrs

Q can complete the work in (8 * 10) hrs=80 hrs

$\inline&space;{\color{Black}\therefore&space;}$ P's 1 hour work=1/96   and Q's 1 hour work= 1/80

(P+Q)'s 1 hour's work =$\inline&space;{\color{Black}&space;\left&space;(&space;\frac{1}{96}+\frac{1}{80}&space;\right&space;)}$ =$\inline&space;{\color{Black}&space;\frac{11}{480}}$

so both P and Q will finish the work in $\inline&space;{\color{Black}&space;\frac{480}{11}}$ hrs

$\inline&space;{\color{Black}&space;\therefore&space;}$ Number of days of 8 hours each = $\inline&space;{\color{Black}&space;\left&space;(&space;\frac{480}{11}&space;\times&space;\frac{1}{8}\right&space;)=\frac{60}{11}}$