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:

Ten women can do a work in six days. Six men can complete the same work in five days. What is the ratio between the capacity of a man and a woman?

 A) 1:2 B) 2:1 C) 2:3 D) 3:2

Explanation:

(10 * 6) women can complete the work in 1 day.

${\color{Black}&space;\therefore&space;}$ 1 woman's  1 day's work =$\inline&space;{\color{Black}&space;\frac{1}{60}&space;}$

(6 * 5) men can complete the work in 1 day.

$\inline&space;{\color{Black}\therefore&space;}$ 1 man's  1 day's work =$\inline&space;{\color{Black}\frac{1}{30}&space;}$

so, required ratio =$\inline&space;{\color{Black}\frac{1}{30}&space;}$ :$\inline&space;{\color{Black}\frac{1}{60}&space;}$ = 2:1

3 1027
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

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.

9 1002
Q:

A and B together finish a wor in 20 days.They worked together for 15 days and then B left. Afer another 10 days,A finished the remaining work. In how many days A alone  can finish the job?

 A) 30 B) 40 C) 50 D) 60

Explanation:

(A+B)'s 15 days work=$\inline&space;{\color{Blue}&space;(\frac{1}{20}\times&space;15)=\frac{3}{4}}$

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

Now, $\inline&space;{\color{Blue}&space;\frac{1}{4}}$ work is done by A in 10 days.

Whole work will bedone by A in $\inline&space;{\color{Blue}&space;(10\times&space;4)=40}$ days.

2 997
Q:

K can build a wall in 30 days. L can demolish that wall in 60 days. If K and L work on alternate days, when will the wall be completed ?

 A) 120 days B) 119 days C) 118 days D) 117 days

Explanation:

K's work in a day(1st day) = 1/30
L's work in a day(2nd day)= -1/60(demolishing)
hence in 2 days, combined work= 1/30 - 1/60
=1/60
since both works alternatively, K will work in odd days and L will work in even days.
1/60 unit work is done in 2 days
58/60 unit work will be done in 2 x 58 days = 116 days
Remaining work = 1-58/60
= 2/60
= 1/30
Next day, it will be K's turn and K will finish the remaining 1/30 work.
hence total days = 116 + 1 = 117.

7 991
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

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

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