Time and Work

Time and Work problems are most frequently asked problems in quantitative aptitude. To solve these problems very quickly, you should understand the concept of Time and Work and some shortcut methods.

If a man can do a piece of work in 5 days, then he will finish 1/5th of the work in one day.

If a man can finish 1/5th of the work in one day then he will take 5 days to complete the work.

If a man 5/6th of work in one hour then he will take 6/5 hours to complete the full work.

If A works three times faster than B then A takes 1/3rd the time taken by B.

Here are some shortcut rules which can be very useful while solving Time and Work problems.

Rule of Flip:

If A can do a piece of work in n days, then the work done by A in one day = 1/n.

If A can repair 50 cycles in 5 days then A can repair 50/5 = 10 cycles in one day.

If A is thrice as good workman as B, then Ratio of work done by A and B = 3:1.Ratio of time taken by A and B to finish a work = 1:3.

If men is fixed, work is proportional to time. If work is fixed, then time is inversely proportional to men therefore,(M1*T1/W1) = (M2*T2/W2)

Total work to be done

Work ability

Work to be done in one day

A take 10 days to complete a job and B takes 20 days to complete the same job. In how much time they will complete the job together ? 1. What is their work efficiency ratio?2. In what time they can do double of the work

Problem-1

3.A started the work and worked for 5 days, after that B entered. Calculate in what time they together finished the remaining work 4. A and B started the work.Before finishing the work ,A left 5 days before. Calculate in what time A and B together worked?

Method-3A(10) B(20)

20-Total Work

21

Work Done By both A and B=20/(2+1)=20/3

A can fill tank in 9 minutes, B can empty the tank in 18 minutes.. In what time the tank be filled, if both pipes work simultaneously?

9 18

18

21

Work Done by both A & B=18/(2-1) =18mins

An inlet pipe can fill the tank in 30 minutes. B an outlet pipe can empty the tank in 45 minutes. In what time the tank be filled if both pipes work simultaneously?

A, B two inlet pipes takes 15,18 minutes to fill the tank and C an oulet pipe takes 45 minutes to empty the tank respectively. In what time the tank be filled if all of them are operated together?

1518

45

90

6

5

2

Time taken by them =90/(6+5-2)=90/9=10 days.

A,B,C can do a work in 15,20,45 days respectively. They get Rs 500 for their work. What is the share of A?

1520

45

180

12

94

Share of A= (ratio of A/total ratios)*total amount=(12/25)*500=240rs.

A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid toC?A.Rs.375B.Rs.400C.Rs.600 D.Rs. 800

6 8

24

4

3

24

1

Share of C=1/8*3200=400/-

X alone can do a piece of work in 15 days and Y alone can do it in 10 days. X and Y undertook to do it for Rs.720. With the help of Z they finished it in 5 days. How much is paid to Z?

A) Rs.360 

B) Rs.120 

C) Rs.240 

D) Rs.300

P and Q can complete a work in 20 days and 12 days respectively. P alone started the work and Q joined him after 4 days till the completion of the work. How long did the work last?A. 5 daysB. 10 daysC. 14 daysD. 22 days

A is twice as efficient as B and can complete a job 30 days before B. In how much time they can complete the job together ?

30

60

60

21

60/(2+1)=20 days

A and B working separately can do a piece of work in 9 and 12 days. If they work a day alternately ,A beginning the work. In how many days work will be completed.

9 12

36

4 3

1 day work of A=41 day work of B=32 days work=4+3=72*5=10 and 7*5=35Remaining work=36-35=1On 11 day A’s turn=1/4Total days to complete a work=10 ¼ days

A and B together can complete a piece of work in 4 days. If A alone complete the work in 12 days. In how many days B alone can do the work.

12

4AB

12A

3 1

B completes the work alone =Total Work/(one day work of AB-one day day work of A)=12/(3-1)=6 days.

A and B can do a piece of work in 21 and 24 days respectively. They started the work together and after some days A leaves the work and B completes the remaining work in 9 days. After how many days did A leave?

A) 5    

B) 7                

C) 8                

D) 6

A and B can complete a piece of work in 18 days. B and C can do it in 24 days. A and C can do it in 36 days. In how many days A,B,C together complete it.

18 2436

4

3

2

72

Work done by A,B,C=[72/(4+3+2)]2=[72/9]2=8*2=16 days.

A, B and C can do a work in 5 days, 10 days and 15 days respectively. They started together to do the work but after 2 days A and B left. C did the remaining work (in days)

A) 1    

B) 3             

C) 5             

D) 4

6 men and 8 women can complete a work in 10 days. 26 men and 48 women can finish the same work in 2 days. 15 men and 20 women can do the same work in - days.

A. 4 days

B. 6 days

C. 2 days

D. 8 days

[6(M) 8(W)]10 days----1

[26M 48W]2days-----2

60 8052 96---------------8 16Inverse=16:8=2:1

Substitute values in 1 or 2[6(2)+8(1)]10=200

15men and 20 women can do work in 15(2)+20(1)=50Number of days=200/50=4days

4 men and 6 women working together can complete the work within 10 days. 3 men and 7 women working together will complete the same work within 8 days. In how many days 10 women will complete this work ? 5 days

(4m---6w)10days-----(I)(3m---7w)8days-------(2)(40 60)10(24 56)8daysSubtract16 4------>reverse the ratio 4:16=1:4Subsitute these values in I[4(1)+6(4)]10=280—total workNumber of days 10 women need=10(4)=40---280/40=7days

5 men or 8 women takes 84 days to complete the work. In how many days does 10 men and 5 women completes the same work?

84*40/10(8)+5(5)=32 days

1 men or 2 women or 3 boys complete a work in 44 days.In how many days does 1 men and 1 women and 1 boy complete the same work

44*6/1(6)+1(3)+1(2)=24 days

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, the time taken by 15 men and 20 boys in doing the same type of work will be:A.4daysB.5daysC.6days D. 7 days

A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?A.8hoursB.10hoursC.12hoursD. 24 hours

If men is fixed, work is proportional to time. If work is fixed, then time is inversely proportional to men therefore, (M1*T1*E1*H1/W1)=(M2*T2*E2*H2/W2)

40 men can cut 60 trees in 8 hours. If 8 men leave the job how many trees will be cut in 12 hours?A. 74B. 82C. 72D. 73

By basic formula:M1 = 40, D1 = 8, W1 = 60(cutting of trees is taken as work)M2 = 40 – 8 = 32, D = 12, W2 = ?Putting the values in the formulaM1 D1/ W1 = M2 D2/ W2We have , 40 x 8 x W2 = 32 x 12 x 60or, W2 = (32 x 12 x 60)/(40 x 8) = 72

If 9 men working 6 hours a day can do a work in 88 days. Then 6 men working 8 hours a day can do it in how many days?(a)98 days(b)99 days(c)100 days(d)102 days

:        From the above formula (m1*t1/w1)=(m2*t2/w2) so (9*6*88/1)=(6*8*d/1)                on solving, d=99 days.