Two people share a task and take certain number of days to complete it. Find the numbers of days required to finish the task individually under the given constraints

1. Pipes and Cisterns Q4

2. Qn: Pipes and Cisterns
(a) 12 days (b) 24 days
(c) 27 days (d) 18 days
A and B together can finish a task in 12 days. If A worked half as
efficiently as he usually does and B works thrice as efficiently as he
usually does, the task gets completed in 9 days. How long would A
take to finish the task if he worked independently?

3. Soln: Pipes and Cisterns
Let A take ‘a’ days to complete the task and B take ‘b’ days to complete the
task.
Thus in one day, A will complete (
1
a
)th of the task.
Similarly in one day, B will complete (
1
b
)th of the task.
So in one day, if A and B work together they will complete (
1
a
+
1
b
) th of the
task.
A and B together can finish a task in 12 days. If A worked half as
efficiently as he usually does and B works thrice as efficiently as he
usually does, the task gets completed in 9 days. How long would A
take to finish the task if he worked independently?

4. Soln: Pipes and Cisterns
Given that A and B together take 12 days to complete the task, then in one
day A and B together complete (
1
12
)th of the task.
Thus,
1
a
+
1
b
=
1
12
……Eqn. 1
If A worked half as efficiently as he usually does, then A will take twice the
time as he usually takes, i.e., 2a days. Thus in one day, A completes (
1
2a
)th of
the task.
A and B together can finish a task in 12 days. If A worked half as
efficiently as he usually does and B works thrice as efficiently as he
usually does, the task gets completed in 9 days. How long would A
take to finish the task if he worked independently?

5. Soln: Pipes and Cisterns
Similarly if B worked thrice as efficiently as he usually does, then B will take
one-third the time he usually takes, i.e.,
b
3
days. Thus in one day, B
completed (
1
b
3
)th or (
3
b
) th of the task.
Thus when both of them work together, they will complete (
1
2a
+
3
b
) th of the
task, given that A and B take 9 days to complete the task.
Thus,
A and B together can finish a task in 12 days. If A worked half as
efficiently as he usually does and B works thrice as efficiently as he
usually does, the task gets completed in 9 days. How long would A
take to finish the task if he worked independently?

6. Soln: Pipes and Cisterns
1
a
+
1
b
=
1
12
……Eqn. 1
1
2a
+
3
b
=
1
9
…… Eqn. 2
A and B together can finish a task in 12 days. If A worked half as
efficiently as he usually does and B works thrice as efficiently as he
usually does, the task gets completed in 9 days. How long would A
take to finish the task if he worked independently?

7. Soln: Pipes and Cisterns
1
2a
+
3
b
=
1
9
…… Eqn. 2
Solving Equations 1 and 2 for ‘a’ we should get the answer,
From equation (1) we get 12(a + b) = ab
From equation (2), we get 9(b + 6a) = 2ab
Substituting ab as 12(a + b) in equation (2) we get 9b + 54a = 2 x 12 x ( a + b)
A and B together can finish a task in 12 days. If A worked half as
efficiently as he usually does and B works thrice as efficiently as he
usually does, the task gets completed in 9 days. How long would A
take to finish the task if he worked independently?

8. Soln: Pipes and Cisterns
9b + 54a = 24a + 24b;
Or, 30a = 15b,
Or, b = 2a
Now, 12(a + b) = ab, or 12 x 3a = 2a2
a = 18 days.
Answer choice (d)
A and B together can finish a task in 12 days. If A worked half as
efficiently as he usually does and B works thrice as efficiently as he
usually does, the task gets completed in 9 days. How long would A
take to finish the task if he worked independently?