Before we move on to the types of problems that you may face in this topic, understand the following formulae -

- If A can do a piece of work in x days, then A’s 1-day work = 1/x
- If A’s one day work is 1/x, A can finish the total work in x days.
- If A is x times as efficient as B then

The ratio of work done by A: B individually = x: 1

The ratio of time taken by A and B individually to finish the work = 1: x

Now let us have a look at the types of problems that you may encounter under this topic -

1. The first type of problem is the most basic one that may be asked - **Calculation of time from work or vice - versa.** For instance -

A takes 8 days to finish a piece of work. B takes 10 days to finish the same work. How long will it take to finish the work when both of them are working together?

Now for such questions, A’s 1-day work = ⅛

B’s 1-day work = 1/10

Work done by both A and B together in one day = ⅛ + 1/10 = 9/40

Hence, A and B together will finish the work in 40/9 days.

Similarly, when n people are involved, you can follow the above approach. For instance,

B and C together can complete the work in 8 days. A and B together can complete the same work in 12 days and A and C together can complete it in 16 days. In how many days can A, B, C can complete the same work?

For this type of question, find the 1-day work of A and B, B and C and A and C.

1-day work of B and C = 1/8 ----- (a)

1-day work of A and B = 1/12 -----(b)

1-day work of A and C = 1/16 -------(c)

Adding (a), (b) and (c),

1-day work of B and C + 1-day work of A and B + 1-day work of A and C = 1/8 + 1/12 + 1/16

2 * (1 day work of A + B + C ) = 13/48

1 day work of A + B + C = (13/48) / 2 = 13/96

So, the number of days taken by A, B, C to finish the work = 96/13.

2. **Another type of problem that you may face is when you need to normalize the time unit**.

A can do a piece of work in 9 days by working 7 hours each day. B can do it in 7 days, working 6 hours per day. How long will it take them to complete the work together if both of them work for 504 minutes per day?

In this type of question, since the time the unit mentioned is not the same for both, so you need to find per hour work of A and B.

A’s 1 hour work = 1/9*7 = 1/63

B’s 1 hour work = 1/7*6 = 1/42

Now, A and B’s one-hour work = (1/63 + 1/42) = 5/126, i.e. they will finish the work in 126/5 hours. But as per the question, they work 504 minutes per day i.e. 504/60 hours per day. So, number of days = (126/5) / (504/60) = 3 days.

3. **Another type of problem that you may face is efficiency-based**. For instance -

X can do a piece of work in 12 days. Y is 80% more efficient than X. How many days will Y take to complete the same work alone.

Now as per question Y does the work 1.8 times more efficiently than X (80% more).

So, ratio of time taken by X : Y = 1.8 : 1 i.e. 12/Y = 1.8/1

Y = 12/1.8 i.e. 20/3 days

4. **Another case that you may face is when one person leaves the work midway**. For instance -

X can finish a piece of work in 18 days and Y can do the same work in 15 days. Y worked for 10 days and left the job. In how many days, X alone can finish the remaining work?

In this case, X’s 1-day work = 1/18, Y’s 1-day work = 1/15

Work done by Y in 10 days = 10 * 1/15 = ⅔

Remaining work = 1 - ⅔ = ⅓

X finishes 1/18th work in 1 day, so he will finish ⅓ work in = (⅓) / (1/18) = 6 days

5. **You may also encounter problems based on wages**. For instance,

X and Y do a piece of work for Rs.600. X alone can do it in 6 days while Y alone can do it in 8 days. With the help of Z, they finish it in 3 days. Find the share of each.

Now, for this question, we’ll find one day work of each and the share of wage will be divided in the ratio of their one day work.

Z’s one day work = ⅓ - (⅙ + ⅛) = 1/24

X : Y : Z = ⅙ : ⅛ : 1/24 = 4 : 3 : 1

Share of X = 600 * (4/8) = 300

Share of Y = 600 * (⅜) = 225

Share of Z = 600 - (300+225) = 75

6. **Another set of problems that you may face is the ones involving more than 2 different types of people**. For instance,

2 women and 3 girls can do a piece of work in 10 days while 3 women and 2 girls can do the same work in 8 days. In how many days can 2 women and 1 girl do the work?

For such questions, let us assume that one woman’s 1-day work = x and 1 girl’s 1-day work = y

Now, 2x + 3y = 1/10 and 3x + 2y = ⅛

You now have two equations in two variables, solve the equations for the values of x and y and accordingly find the answer.

So, these are the possible variants of this topic that you may face in the exams. If you find it useful, **do share the article with your friends on Facebook or through any other channel.** We'll keep posting exam oriented topics with examples whenever possible, so, stay tuned for more updates..!!

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