Here are important formulas and shortcuts to solve problems related to time and work. Basic knowledge
regarding work done by given persons in specific time and related problems is important for various competitive exams like IBPS,
SBI Bank PO, assistant, SSC exams, Railway exam, UPSC exams.

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**Important Fact:**

- If A can do a work in N days, A's 1 day's work = (1/N).

**Case I:**

**If A can finish a work in M hours and B can finish same work in N hours. Working together, independently they will finish the job in (MN) / (M+N) hours.**

**If A can finish a work in L hours, B can finish same work in M hours and C can finish same work in N hours. Working together, independently they will finish the job in (LMN) / (LM+MN+NL) hours.**

**Derivation: (Show/Hide)**

**Eg:**If A can finish a work in 5 hours and B can finish the same work in 7 hours. How long should it take both A and B, working together but independently, to do the same job?

**Soln:**Here M = 5, N = 7

Hence A and B can finish same work in (5 x 9) / (5 + 9) hours = 45/14 hours = 3 {3/14} hours.

**Case II:**

**If A and B can finish a work in M days and A alone can finish the same work in N days. Than B alone can complete that work in (MN)/ (N - M) days.**

**Eg:**A and B together can complete a piece of work 9 days. If A alone can finish the same work in 15 days, in how many days can B complete the same work?

**Soln:**Here M = 9, N = 15

Hence B can finish the work in (9 x 15) / (15 - 9) days. = 45 / 6 = 22 { 1 / 2} days.

**Case III:**

**A and B can finish a work in K days. B and C can finish the same work in M. A and C can finish the same work in N days.**

Working together they all can finish the work in (A + B + C):

**X = (2LMN) / (LM + MN + NL)**days.

A alone can finish same work in

**(XM) / (X - M)**days.

B alone can finish same work in

**(XN) / (X - N)**days.

C alone can finish same work in

**(XL) / (X - L)**days.

**Case IV:**

**If A is thrice as good a workman as B,**

Ratio of work done by A and B = 3 : 1

Time taken by A and B to finish a work = 1 : 3

If A can finish a work in M days,

B can finish same work in (M x 3) days.

A and B working together can finish same work in (M x M x 3) / (M + 3M) days.

**Eg.**A is thrice as good a workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:

**Soln:**Working together they can finish work in: (60 x 60 x 3) / (60 + 180) = 45 Days.

**Case V:**

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

Soln: Let 1 men's 1 day work = x and 1 women's i day's work = y.

Then 2x + 3y = 1 / 10 and 3x + 2y = 1 / 8

Solving we get: x = 7 / 200 and y = 1 / 100

2 men and 1 women can finish the work in 25 / 2 days.

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