x's and y's introduced into any topic can complicate anything, including pipes and tanks

1. Pipes Cisterns

2. Pipes Cisterns
Consider three friends A, B and C who work at differing speeds.
When the slowest two work together they take n days to finish a
task. When the quickest two work together they take m days to
finish a task. One of them, if he worked alone would take thrice as
much time as it would take when all three work together. How much
time would it take if all three worked together?
(a)
3mn
2(m + n)
(b)
2mn
m + n
(c)
4mn
3(m + n)
(d)
5mn
3(m + n)

3. Pipes Cisterns
Let A < B < C in terms of efficiency.
B and C together take n days.
A and B together take m days.
Consider three friends A, B and C who work at differing speeds.
When the slowest two work together they take n days to finish a
task. When the quickest two work together they take m days to
finish a task. One of them, if he worked alone would take thrice as
much time as it would take when all three work together. How much
time would it take if all three worked together?

4. Pipes Cisterns
One of them, if he worked alone would take thrice as much time as it
would take when all three work together. This is a crucial statement.
Now, if there are three people who are all equally efficient, for each
of them it would take thrice as much time as for all three together.
Consider three friends A, B and C who work at differing speeds.
When the slowest two work together they take n days to finish a
task. When the quickest two work together they take m days to
finish a task. One of them, if he worked alone would take thrice as
much time as it would take when all three work together. How much
time would it take if all three worked together?

5. Pipes Cisterns
Now, this tells us that the person who takes thrice as much time
cannot be the quickest one. If the quickest one is only one-third as
efficient as the entire team, the other two cannot add up to two-
thirds. By a similar logic, the slowest one cannot be the person who
is one-third as efficient.
Consider three friends A, B and C who work at differing speeds.
When the slowest two work together they take n days to finish a
task. When the quickest two work together they take m days to
finish a task. One of them, if he worked alone would take thrice as
much time as it would take when all three work together. How much
time would it take if all three worked together?

6. Pipes Cisterns
In other words, the person one-third as efficient = B
Let A, B and C together take x days. B alone would take 3x days
B and C together take n days. Or B + C in 1 day do
1
n
of the task ........Eqn (i)
Consider three friends A, B and C who work at differing speeds.
When the slowest two work together they take n days to finish a
task. When the quickest two work together they take m days to
finish a task. One of them, if he worked alone would take thrice as
much time as it would take when all three work together. How much
time would it take if all three worked together?

7. Pipes Cisterns
A and B together take m days. Or, A + B in 1 day do
1
m
of the task ........Eqn (ii)
B takes 3x days to do the task. Or, B, in one day, does
1
3x
of the task ........Eqn (iii)
Consider three friends A, B and C who work at differing speeds.
When the slowest two work together they take n days to finish a
task. When the quickest two work together they take m days to
finish a task. One of them, if he worked alone would take thrice as
much time as it would take when all three work together. How much
time would it take if all three worked together?

8. Pipes Cisterns
Now, if we do (i) + (i) – (iii) we get
A + B + C do
1
n
+
1
m
-
1
3x
in a day. This should be equal to
1
x
as all three
of them complete the task in x days.
1
n
+
1
m
-
1
3x
=
1
x
Consider three friends A, B and C who work at differing speeds.
When the slowest two work together they take n days to finish a
task. When the quickest two work together they take m days to
finish a task. One of them, if he worked alone would take thrice as
much time as it would take when all three work together. How much
time would it take if all three worked together?

9. Pipes Cisterns
1
n
+
1
m
=
4
3x
m + n
mn
=
4
3x
x =
4mn
3(m + n)
. Answer choice (c)
Consider three friends A, B and C who work at differing speeds.
When the slowest two work together they take n days to finish a
task. When the quickest two work together they take m days to
finish a task. One of them, if he worked alone would take thrice as
much time as it would take when all three work together. How much
time would it take if all three worked together?

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