# 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 and B can do a piece of work in 40 and 50 days. If they work at it an alternate days with A beginning in how many days, the work will be finished ?

(A+B)'s two days work = $140+150=9200$

Evidently, the work done by A and B duing 22 pairs of days

i.e in 44 days = $22×9200=198200$

Remaining work = $1-198200$= 1/100

Now on 45th day A will have the turn to do 1/100 of the work and this work A will do in $40×1100=25$

Therefore,  Total time taken = 44$25$daya

Subject: Time and Work
Job Role: Bank PO

26205
Q:

A and B together can do a piece of work in 40 days. A having worked for 20 days, B finishes the remaining work alone in 60 days. In How many days shall B finish the  whole work alone?

 A) 60 B) 70 C) 80 D) 90

Explanation:

Let A's 1 day's work=x and B's 1 day's work=y

Then x+y = 1/40 and 20x+60y=1

Solving these two equations , we get : x= 1/80 and y= 1/80

Therefore B's  1 day work = 1/80

Hence,B alone shall finish the whole work in 80 days

Filed Under: Time and Work

32 24923
Q:

A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days  ?

 A) 9 days B) 11 days C) 13 days D) 15 days

Explanation:

Ratio of times taken by A and B = 100 : 130 = 10 : 13.
Suppose B takes x days to do the work.

Then, 10 : 13 :: 23 : x     =>     x = ( 23 x 13/10 )     =>     x = 299 /10.

A's 1 day's work = 1/23 ;
B's 1 day's work = 10/299 .

(A + B)'s 1 day's work = ( 1/23 + 10/299 ) = 23/299 = 113 .

Therefore, A and B together can complete the work in 13 days.

Filed Under: Time and Work
Exam Prep: AIEEE , Bank Exams , CAT , GATE
Job Role: Bank Clerk , Bank PO

52 24715
Q:

If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days what is time taken by 15 men and 20 boys?

 A) 4 days B) 6 days C) 7 days D) 5 days

Explanation:

Given that

6 men and 8 boys can do a piece of work in 10 days

26 men and 48 boys can do the same in 2 days

As the work done is equal,

10(6M + 8B) = 2(26M + 48B)

60M + 80B = 52M + 96B

=> M = 2B

=> B = M/2 ……(1)

Now Put (1) in 15M + 20B

=> 15M + 10M = 25M

Now, 6M + 8B in 10 days

=> (6M + 4M) 10 = 100M

Then D(25M) = 100M

=> D = 4 days.

Filed Under: Time and Work
Exam Prep: GATE , CAT , Bank Exams , AIEEE
Job Role: Bank PO , Bank Clerk

32 24152
Q:

A is twice efficient as B and together they do the same work in as much time as C and D together. If C and D can complete the work in 20 and 30 daysrespectively, working alone ,then in how many days A can complete the work individually:

 A) 12 days B) 18 days C) 24 days D) 30 days

Explanation:

A     +      B        =      C     +     D

|              |                 |             |

Ratio of efficiency         10x   +    5x               9x     +   6x

|________|                 |_________|

15x                           15x

Therefore , ratio of efficiency of A:C  =10:9

Therefore,  ratio of days taken by A:C = 9:10

Therefore, number of days taken by A = 18 days

Filed Under: Time and Work

54 23425
Q:

A does half as much work as Band C does half as much work as A and B together. If C alone can finish the work in 40 days, then together ,all will finish the work in  ?

 A) 17 + 4/7 days B) 13 + 1/3 days C) 15 + 3/2 days D) 16 days

Explanation:

C alone can finish the work in 40 days.
As given C does half as much work as A and B together
=> (A + B) can do it in 20 days
(A + B)s 1 days wok = 1/20.
A's 1 days work : B's 1 days Work = 1/2 : 1 = 1:2(given)
A's 1 day’s work = (1/20) x (1/3) = (1/60) [Divide 1/20 in the raio 1:2]
B's 1 days work = (1/20) x (2/3) = 1/30
(A+B+C)'s 1 day's work = (1/60) + (1/30) + (1/40) = 9/120 = 3/40

All the three together will finish it in 40/3 = 13 and 1/3 days.

Filed Under: Time and Work
Exam Prep: AIEEE , Bank Exams , CAT , GATE , GRE
Job Role: Bank Clerk , Bank PO

46 23294
Q:

A group of workers was put on a job. From the second day onwards, one worker was withdrawn each day. The job was finished when the last worker was withdrawn. Had no worker been withdrawn at any stage, the group would have finished the job in 55% of the time. How many workers were there in the group?

 A) 50 B) 40 C) 45 D) 10

Explanation:

Let the number of workers be x.

Now, Using work equivalence method,

X + (X-1) + (X-2)+ . . . . + 1 = X *55% of X

=> [X * (X+1)] / 2 = X * (55X/100)    [because, Series is in AP. Sum of AP = {No. of terms (first term+ last term)/2} ]

Therefore, X = 10

Filed Under: Time and Work

63 23071
Q:

9 men and 12 boys finish a job in 12 days, 12 men and 12 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days ?

 A) 15 days B) 11 days C) 14 days D) 12 days

Explanation:

9M + 12B ----- 12 days ...........(1)
12M + 12B ------- 10 days........(2)
10M + 10B -------?
108M + 144B = 120M +120B
24B = 12M => 1M = 2B............(3)

From (1) & (3)

18B + 12B = 30B ---- 12 days

20B + 10B = 30B -----? => 12 days.