Shortcut:
If P and Q can do a piece of work in x days, Q and R in y days, R and P in z days, then (P + Q + R) working together will do the same work in
2xyz
/
xy + yz + zx
days.
Let we denote t =
2xyz
/
xy + yz + zx
then
P alone will do the same work in
yt
/
y − t
days
Q alone will do the same work in
zt
/
z − t
days
R alone will do the same work in
xt
/
x − t
days
Here, x = 12, y = 15, z = 20
Using these values in the shortcut, we get:
t =
2 x 12 x 15 x 20
/
180 + 300 + 240
=
2 x 12 x 15 x 20
/
720
= 10
Hence, A + B + C will take 10 days.
Now, A can do the work in
10 x 15
/
15 − 10
= 30 days
Now, B can do the work in
10 x 20
/
20 − 10
= 20 days
Now, C can do the work in
10 x 12
/
12 − 10
= 60 days
