**Case : 1**If A can do a piece of work in x days

B can do same piece of work in y days

Then if A & B will work together then time = xy/x+y days

**Case : 2**If A & B can do a piece of work in x days

and A alone can do same work in y days

Then B alone can do same piece of work in

= xy/(x-y)

**Case :3**If A can do the work in x days,

B can do the same work in y days,

& C can do the same work in z days,

Then time taken by them when they will work together = xyz/(x+y+z)

**Case : 4**if A and B can do a work in x days

If B and C can do a work in y days

if C and A can do a work in z days

Then time taken by them when they will work together = 2xyz/(xy+yz+zx)

**Case :5**A and B can do a work in a and b days respectively

Both begin together but after some days, A leaves off and the remaining work is completed by B in x days.

Then the time after which A left is given by = (b-x)a/a+b

**Example :**A man and a women can do a piece of work in 30 days and 40 days respectively. Both begin together but after a certain day the man leaves off. In this case, the woman finishes the remaining work in 10 days, after how many days did the man leave ?

**Solution :**This is Case no. 5 so a = 30 days, b = 40 days, x = 10 days Required time = (b-x)a/a+b

= (40-10)30/70

= 900/70 = 9/7 days

**Case : 6**When two different(like man & moman or man & boys) work together then , find the ratio between two person like person 1 = x.person 2

Better can understand by an example :

**Ques : 10 men & 6 boys can complete the task in 20 days while 12 men & 4 boys can complete the work in 18 days find how many days it will take 8 men & 8 boys to complete the same work ?**

**Answer :**

10 Men & 6 Boys =====20 Days

(10*20 200) (6*20 120) ………………(1)

12 Men & 4 Boys ====== 18 Days

(12*18 216) (18*4 72) ………………(2)

Subtract equ (1) & equ(2) to get the ration between men & boys

16 : 48

Means 1 : 3 (1 men = 3 boys)

So

8 men = 24 boys

So 24+8 = 32 boys

Let x is time taken by 32 boys to complete the task ====

32*x = = 36*20

X === 45/2 days

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