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

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

Hence,

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 = $\frac{100}{Efficiency}$

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 =  = 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

95 33545
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 =1/96 ; 1 woman's 1 day work = 1/192

Work done in 6 days=

Remaining work = 1/4

(8 men +8 women)'s 1 day work = $1\left(\frac{8}{96}+\frac{8}{192}\right)$ =1/8

Remaining work =1/4 -  1/8 = 1/8

1/96 work is done in 1 day by 1 man

Therefore, 1/8 work will be done in 1 day by 96 x (1/8) =12 men

65 22413
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.

44 21226
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?

Ratio of times taken by A and B = 1 : 2.

The time difference is (2 - 1) 1 day while B take 2 days and A takes 1 day.

If difference of time is 1 day, B takes 2 days.

If difference of time is 30 days, B takes 2 x 30 = 60 days.

So, A takes 30 days to do the work.

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

B's 1 day's work = 1/60

(A + B)'s 1 day's work = 1/30 + 1/60 = 1/20

A and B together can do the work in 20 days.

23854
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 = $\frac{25x}{175x}×100$ % = $14\frac{2}{7}%$

29 6614
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= 1/20 + 1/60 = 1/15

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

Therefore,  we get: 2 x (A's 1 day 's work)=1/15

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

Therefore, B's 1 day's work= 1/20 - 1/30 = 1/60

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

26 8956
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 = 1/30 + 1/24 + 1/20 = 1/8

=>(A+B+C)'s  1 day's work= 1/16

work done by A,B and C in 10 days=10/16 = 5/8

Remaining work= 3/8

A's 1 day's work= $\left(\frac{1}{16}-\frac{1}{24}\right)=\frac{1}{48}$

Now, 1/48 work is done by A in 1 day.

So, 3/8 work  wil be done by A in =48 x (3/8) = 18 days

18 10678
Q:

The ratio of efficiency of A is to C is 5:3. The ratio of number of days taken by B is to C is 2:3. A takes 6 days less than C, when A and C completes the work individually. B and C started the work and left after 2 days. The number of days taken by A to finish the remaining work is:

 A) 4.5 B) 5 C) 6 D) 9 1/3

Explanation:

A   :   C

Efficiency      5    :   3

No of days   3x   :  5x

Given that, 5x-6 =3x  => x = 3

Number of days taken by A = 9

Number of days taken by C = 15

B  :  C

Days   2  :  3

Therefore, Number of days taken by B = 10

Work done by B and C in initial 2 days = $2\left[\frac{1}{10}+\frac{1}{15}\right]$= 1/3

Thus,  Rest work =2/3

Number of days required by A to finish 2/3 work = (2/3) x 9 = 6 days