Questions on Time and work done are the most commonly asked ones in most of the exams, say SSC, RRB, Banking exams. To approach this problem the first thing that we need to understand is a very basic concept: more people take less time to finish a work and less number of people take more time to complete a work. To explain it further, let us assume that we assigned a task to one particular person and asked him to finish the job in x number of days. What if you see that the person is not able to finish it in x days, you add more workers so that it is completed on the specified date. Now, let us take a look at the concepts and tricks to solve time and work for Bank, SSC, RRB exam.

#### Points to remember:

If A can do a piece of work in n days, then A’s one day’s work = **1/n**

Assume A’s one day’s work is **1/n**, then A can finish the work in **n days**.

If A is thrice as good a 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**

**Time and Work Problems**

**1. If Roger can do a piece of work in 8 days and Antony can complete the same work in 5 days, in how many days will both of them together complete it?**

Ans.: Roger’s 1 day’s work = 1/8

Antony’s 1 day’s work = 1/5

(Roger +Antony’s) 1 day’s work = (1/8)+(1/5) = 13/40

Therefore, both Roger and Antony will complete the work in 40/13 = 3 and 1/3 days.

**Another approach:**

Roger’s can do a work in 8 days.

Antony can do the work in 5 days.

Find out the LCM of 8 and 5 = 40

So, work done by roger in a day = 40/8 = 5

work done by Antony in a day = 40/5 = 8

So total work in one day = 8 + 5 = 13.

So the total time taken by them to complete the work = 40/13 = 3 and 1/3 days.

**2. A and B together can complete a piece of work in 15 days and B alone in 20 days. In how many days can A alone complete the work? **

Ans.: (A+B)’s 1 day’s work = 1/15

B’s 1 day’s work = 1/20

Therefore, A’s 1 day’s work = 1/15 – 1/20 = 1/60.

Hence, A alone can complete the work in 60 days.

**3. A alone can complete a piece of work of Rs.300 in 6 days; but by engaging an assistant, the work is completed in 4 days. Find the share to be received by the assistant. **

Ans.: Assistant’s 1 day’s work = (1/4) – (1/6) = 1/12

Therefore, A’s share : Assistant’s share = Ratio of their 1 day’s work= (1/6) : (1/12) = 2 : 1

Hence, assistant’s share = Rs. (300 x (1/3) ) = Rs.100.

**4. A and B can do a piece of work in 9 days, B and C can do it in 12 days; A and C can do it in 18 days. In how many days will A,B and C finish it, working together and separately. **

Ans.: (A+B)’s 1 day’s work = 1/9

(B+C)’s day’s work = 1/12

(A+C)’s 1 day’s work = 1/18

On addition, we get,

2 ( A+B+C)’s work = (1/9)+(1/12)+(1/18) = (9/36) = ¼

( A+B+C)’s 1 day’s work = 1/8

Thus, A, B and C together can finish the work in 8 days.

Now, A’s 1 day’s work = ((A+B+C)’s one day’s work – (B+C)’s one day’s work)

= (1/8)-(1/12) = 1/24

Therefore, A alone can finish the work in 24 days.

Similarly, B’s one day’s work = ((A+B+C)’s 1 day’s work – (A+C)’s one day’s work)

= (1/8) – (1/18) = 5/72.

Therefore, B alone can finish the work in 72/5 = 14 and 2/5 days.

And, C’s one day’s work – ((A+B+C)’s 1 day’s work –(A+B)’s 1 day’s work)

= (1/8) – (1/9) = 1/72

Therefore, C can finish the work in 72 days.

**5. A can complete a work in 10 days, B in 12 days and C in 15 days. All of them began the work together, but A had to leave the work after 2 days of the start and B, 3 days before the completion of the work, How long did the work last? **

Ans,: A, B and C work together for 2 days. C alone works for 3 days and the remaining work is done by B and C together.

(A+B+C)’s two day’s work = 2 ((1/10)+(1/12)+(1/15)) = ½

C’s 3 day’s work = ( 3 x (1/15) ) = 1/5

Remaining work = 1 – ((1/2)+(1/5)) = 3/10

But, (B+C)’s 1 day’s work = (1/12) + (1/15) = 3/20.

Now, 3/20 is done by (B+C) in 1 day.

Therefore, 3/10 work is done by (B+C) in (20/3) x (3/10) = 2 days.

Hence, total time taken = 2+3+2 days = 7 days.

**6. Ayesha can complete a piece of work in 16 days. Amrita can complete the same piece of work in 8 days. If both of them work together in how many days can they complete the same piece of work? **

Ans.: Ayesha’s 1 day’s work = 1/16

Amita’s one day’s work = 1/8

(Ayesha + Amita)’s 1 day’s work = (1/16)+(1/8) = 3/16.

Therefore, both can complete the work in 16/3 = 5 and 1/3 days.

**7. Nine children can complete a piece of work in 360 days. 18 men can complete the same piece of work in 72 days and 12 women can complete it in 162 days. In how many days can 4 men,12 women and 10 children together complete the piece of work?**

Ans.: 1 man’s 1 day’s work = 1 / (72 x 18) = 1 /1296

One woman’s one day’s work = 1/ (162×12) = 1/1944

1 child’s 1 day’s work = 1/(360×9) = 1/3240

(4 men + 12 women + 10 children)’s one day’s work

= (4 x (1/1296)) + (12 x (1/1944)) + (10 x (1/3240)

= 1/81

Hence, 4 men, 12 women and 10 children can complete the work in 81 days.

**8. 10 persons begin to work together on a job but after some days 4 persons leave. As a result, the job which could have been completed in 40 days is completed in 50 days. How many days after the commencement of the work did the 4 persons leave?** **(SSC, 2004)**

Ans.: 10 person’s can complete the work in 40 days.

Therefore, one person’s one day’s work = 1/(40 x 10) = 1/400

Suppose 4 persons left after n days

Then, ((1/ 400) x 10 x n ) + (1/400) x 6x (50-n))=1

(1/40)n + (3/200)(50-x) = 1

(1/100)n = 1/4

n = 25.

**9. A can knit a pair of socks in 3 days. B can knit the same pair in 9 days. If they are knitting together, then in how many days will they knit two pairs of socks. (RRB, 2004)**

Ans. Number of pairs knit by A and B together in 1 day = (1/3) + (1/9) = 4/9

Therefore, the required number of days = (2 x (9/4))= 4 and (1/2) days

**10. A man and a boy together can do a certain amount of digging in 40 days. Their speeds in digging are in the ratio of 8:5. How many days will the boy take to complete the work if engaged alone? (RRB, 2005)**

Ans.: Ratio of digging speeds of man and boy = 8:5

Ratio of times by man and boy = 5:8

Suppose the man takes 5x days while the boy takes 8x days to complete the work alone.

Then,

(1/(5x)) + (1/(8x)) = 1/40

X = 13

Hence, time taken by the boy to complete the work alone = 8 x 13 days = 104 days.

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