**Time and Work Notes: Short Tricks To Solve time & work questions**

**Time And Work Formula & Tricks**

**When work is same.**

**Time∝1/Efficiency**

**If A can do a piece of work in n days.**

**Then, per day working efficiency of A = 1/n**

**If working efficiency of A & B is → x : y.**

**Then, the time taken by A & B to finish the work is in the ratio → y : x**

- If A can do a piece of work is x days and B can do a piece of work in y days, then both of them working together will do the same work in

**xy/(x+y) days**

__Explanation__**Q. A can finish a piece of work by working alone in 6 days and B, while working alone, can finish the same work in 12 days. If both of them work together, then in how many days, the work will be finished?**

**Sol.**x = 6, y = 12

**If A, B & C will working alone, can complete a work in x, y and z days, respectively, then they will together complete the work in**

**xyz/(xy+yz+zx)**

__Explanation__

**Q. A, B, and C can complete a piece of work in 10, 15 and 18 days, respectively. In how many days would all of them complete the same work working together?**

**Sol.**x = 10 days, y = 15 days & z = 18 days

**Two persons A & B, working together, can complete a piece of work in x days. If A, working alone, can complete the work in y days, then B, working alone, will complete the work in**

**⇒xy/(y-x)**

__Explanation__

**Q. A and B working together take 15 days to complete a piece of work. If A alone can do this work in 20 days, how long would B take to complete the same work?**

**Sol.**x = 15, y = 20

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**If A & B working together, can finish a piece of work is x days, B & C in y days, C & A in z days. Then, A + B + C working together will finish the job is**

**⇒2xyz/(xy+yz+zx)**

__Explanation__

**Q. A and B can do a piece of work in 12 days, B and C in 15 days, C and A in 20 days. How long would they take to complete the full work together?**

**Sol.**x = 12 days, y = 15 days, z = 20 days

**If A can finish a work in x days and B is k times efficient than A, then the time taken by both A and B, working together to complete the work is**

**x/(1+k)**

__Explanation__

**Q. Harbans Lal can do a piece of work in 24 days. If Bansi Lal works twice as fast as Harbans Lal, how long would they take to finish the work working together?**

**Sol.**x = 24, k = 2

**If A & B working together can finish a work in x days & B is k times efficient than A, then the time taken by,**

**A working Alone will take ⇒ (k + 1) x**

**B working Alone will take ⇒ ((k+1)/k)x**

__Explanation__

**Q. A and B together can do a piece of work in 3 days. If A does thrice as much work as B in a given time, find how long A alone would take to do the work?**

**Sol**. x = 3, k = 3

**If A working Alone takes a days more than A & B, & B working Alone takes b days more than A & B. Then ,**

**Number of days, taken by A & B working together to finish a job is = √ab**

__Explanation :__

**Q. A alone would take 8 hrs more to complete the job than if both A and B worked together. If B worked alone, he took 41/2 hrs more to complete the job than A and B worked together. What time would they take if both A and B worked together?**

**Sol.**a = 8, b = 9/2

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