# Time and Work Formula

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