SHORTCUT OF THE DAY
Two persons A and B can a finsh a job alone in x and y days
respectively.if they start working alternate days,then to find the total job
completion time following steps are
taken.
Note:This formla applicable only when x and y are integers.
Case:If A starts the work
Step I:first caluculate the value of p; nearest integer
value to be considerd=(xy/x+y)
Step II:
a)when, x-y=+or- 2, +or-4 then apply the following formla.
T(total job completion time)=xy+p(x-y)/x
b)when, x-y=+or- 1, +or-3 then apply the following formla.
T(total job completion time)=xy-p(x-y)/y
Eg1: Two persons A and B can a finsh a job alone in 5 and 7
days respectively.if they start working alternate days,If A starts the work then to find the total job completion
time
Ans: Applying the above shortcut
StepI:p=xy/x+y=5*7/5+7=35/12=3(nearest integer value)
Step II:x-y=5-7=-2, here the formula (a) applied
Total time(If A starts the work)=xy+p(x-y)/x=5*7+3(5-7)/5
=29/5=5 4/5
Eg2: Two persons A and B can a finsh a job alone in 9 and 12
days respectively.if they start working alternate days,If A starts the work then to find the total job completion
time
Ans: Applying the above shortcut
StepI:p=xy/x+y=9*12/9+12=108/21=5(nearest integer value)
Step II:x-y=9-12=-3, here the formula (a) applied
Total time(If A starts the work)=xy-p(x-y)/y=9*12-5(9-12)/12
=41/4=10 ¼ days
if u have any doughts about this shortcut comment here.........
