This one is a word problem in work time. A rates problem solving question the way it is typically tested in the GMAT quant section. It is a simple question. The explanation provides a concise explanation on how to solve such questions and provides a detailed solution to the question. A and B working together complete a task in 12 days. If B alone takes 60 days to complete the task, how long will A alone take to complete the task? A) 30 days B) 18 days C) 20 days D) 24 days E) 15 days

1. GMAT QUANTITATIVE REASONING
WORD PROBLEMS
RATES – WORK TIME
PROBLEM SOLVING
Diagnostic Test

2. Question
A and B working together complete a task in 12 days. If B
alone takes 60 days to complete the task, how long will A
alone take to complete the task?
A. 30 days
B. 18 days
C. 20 days
D. 24 days
E. 15 days

3. Step 1
How to approach work time questions?

4. Understanding relation between time taken and rate01
How long will A alone take to complete the task?
A and B working together take 12 days. B alone takes 60 days

5. Understanding relation between time taken and rate
· If A takes ‘a’ days to complete a task
01
How long will A alone take to complete the task?
A and B working together take 12 days. B alone takes 60 days

6. Understanding relation between time taken and rate
· If A takes ‘a’ days to complete a task A will complete
1
a
of the task in a day
01
How long will A alone take to complete the task?
A and B working together take 12 days. B alone takes 60 days

7. Understanding relation between time taken and rate
· If A takes ‘a’ days to complete a task A will complete
1
a
of the task in a day
Therefore, if A takes 20 days and B takes
30 days to complete a task, it will be
absurd to say that working together they
will take 20 + 30 = 50 days.

01
How long will A alone take to complete the task?
A and B working together take 12 days. B alone takes 60 days

8. Understanding relation between time taken and rate
· If A takes ‘a’ days to complete a task A will complete
1
a
of the task in a day
Therefore, if A takes 20 days and B takes
30 days to complete a task, it will be
absurd to say that working together they
will take 20 + 30 = 50 days.
  In a day A will complete
1
20
th of the task and
B will complete
1
30
th of the task.
Together they will complete
1
20 +
1
30 =
3+2
60 =
1
12
Or they will complete the task in 12 days.
01
How long will A alone take to complete the task?
A and B working together take 12 days. B alone takes 60 days

9. Understanding relation between time taken and rate. Continued….01
How long will A alone take to complete the task?
A and B working together take 12 days. B alone takes 60 days

10. Understanding relation between time taken and rate. Continued….
Similarly, if A takes ‘a’ days to complete a
task and B takes ‘b’ days to complete a
task and if working together they will
complete the task in 10 days,
it is INCORRECT to say a + b = 10.

01
How long will A alone take to complete the task?
A and B working together take 12 days. B alone takes 60 days

11. Understanding relation between time taken and rate. Continued….
Similarly, if A takes ‘a’ days to complete a
task and B takes ‘b’ days to complete a
task and if working together they will
complete the task in 10 days,
it is INCORRECT to say a + b = 10.
  The correct expression is
1
a +
1
b =
1
10
01
How long will A alone take to complete the task?
A and B working together take 12 days. B alone takes 60 days

12. Understanding relation between time taken and rate. Continued….
Only the rate of work done in a day by two people
working together can be added or subtracted. The time
taken individually should not be added or subtracted.
Similarly, if A takes ‘a’ days to complete a
task and B takes ‘b’ days to complete a
task and if working together they will
complete the task in 10 days,
it is INCORRECT to say a + b = 10.
  The correct expression is
1
a +
1
b =
1
10
01
How long will A alone take to complete the task?
A and B working together take 12 days. B alone takes 60 days

13. Step 2
Frame equation; solve equation

14. How long will A alone take to complete the task?
A and B working together take 12 days. B alone takes 60 days
· Working alone, let A take ‘a’ days to complete the
task.

15. How long will A alone take to complete the task?
A and B working together take 12 days. B alone takes 60 days
· Working alone, let A take ‘a’ days to complete the
task.
A will complete
1
a
of the task in a day.

16. How long will A alone take to complete the task?
A and B working together take 12 days. B alone takes 60 days
· Working alone, let A take ‘a’ days to complete the
task.
A will complete
1
a
of the task in a day.
· Working alone, B take 60 days to complete the
task.

17. How long will A alone take to complete the task?
A and B working together take 12 days. B alone takes 60 days
· Working alone, let A take ‘a’ days to complete the
task.
A will complete
1
a
of the task in a day.
· Working alone, B take 60 days to complete the
task.
B will complete
1
60
of the task in a day.

18. How long will A alone take to complete the task?
A and B working together take 12 days. B alone takes 60 days
· Working alone, let A take ‘a’ days to complete the
task.
A will complete
1
a
of the task in a day.
· Working alone, B take 60 days to complete the
task.
B will complete
1
60
of the task in a day.
· Working together A and B will complete
1
a
+
1
60
of
the task in a day.

19. How long will A alone take to complete the task?
A and B working together take 12 days. B alone takes 60 days
· Working alone, let A take ‘a’ days to complete the
task.
A will complete
1
a
of the task in a day.
· Working alone, B take 60 days to complete the
task.
B will complete
1
60
of the task in a day.
· Working together A and B will complete
1
a
+
1
60
of
the task in a day.
Working together A and B take 12 days.

20. How long will A alone take to complete the task?
A and B working together take 12 days. B alone takes 60 days
· Working alone, let A take ‘a’ days to complete the
task.
A will complete
1
a
of the task in a day.
· Working alone, B take 60 days to complete the
task.
B will complete
1
60
of the task in a day.
· Working together A and B will complete
1
a
+
1
60
of
the task in a day.
Working together A and B take 12 days.
 they complete
1
12
of the task in a day .

21. How long will A alone take to complete the task?
A and B working together take 12 days. B alone takes 60 days
· Working alone, let A take ‘a’ days to complete the
task.
A will complete
1
a
of the task in a day.
· Working alone, B take 60 days to complete the
task.
B will complete
1
60
of the task in a day.
· Working together A and B will complete
1
a
+
1
60
of
the task in a day.
Working together A and B take 12 days.
·
 they complete
1
12
of the task in a day .
Equating the two,
1
a
+
1
60
=
1
12

22. How long will A alone take to complete the task?
A and B working together take 12 days. B alone takes 60 days
· Working alone, let A take ‘a’ days to complete the
task.
A will complete
1
a
of the task in a day.
· Working alone, B take 60 days to complete the
task.
B will complete
1
60
of the task in a day.
· Working together A and B will complete
1
a
+
1
60
of
the task in a day.
Working together A and B take 12 days.
·
 they complete
1
12
of the task in a day .
Equating the two,
1
a
+
1
60
=
1
12 Or
1
a
=
1
12
-
1
60

23. How long will A alone take to complete the task?
A and B working together take 12 days. B alone takes 60 days
· Working alone, let A take ‘a’ days to complete the
task.
A will complete
1
a
of the task in a day.
· Working alone, B take 60 days to complete the
task.
B will complete
1
60
of the task in a day.
· Working together A and B will complete
1
a
+
1
60
of
the task in a day.
Working together A and B take 12 days.
·
 they complete
1
12
of the task in a day .
Equating the two,
1
a
+
1
60
=
1
12 Or
1
a
=
1
12
-
1
60
1
a
=
5 - 1
60
=
4
60
=
1
15

24. A takes 15 days
How long will A alone take to complete the task?
A and B working together take 12 days. B alone takes 60 days
· Working alone, let A take ‘a’ days to complete the
task.
A will complete
1
a
of the task in a day.
· Working alone, B take 60 days to complete the
task.
B will complete
1
60
of the task in a day.
· Working together A and B will complete
1
a
+
1
60
of
the task in a day.
Working together A and B take 12 days.
·
 they complete
1
12
of the task in a day .
Equating the two,
1
a
+
1
60
=
1
12 Or
1
a
=
1
12
-
1
60
1
a
=
5 - 1
60
=
4
60
=
1
15

25. Correct Answer : Choice E
A takes 15 days
How long will A alone take to complete the task?
A and B working together take 12 days. B alone takes 60 days
· Working alone, let A take ‘a’ days to complete the
task.
A will complete
1
a
of the task in a day.
· Working alone, B take 60 days to complete the
task.
B will complete
1
60
of the task in a day.
· Working together A and B will complete
1
a
+
1
60
of
the task in a day.
Working together A and B take 12 days.
·
 they complete
1
12
of the task in a day .
Equating the two,
1
a
+
1
60
=
1
12 Or
1
a
=
1
12
-
1
60
1
a
=
5 - 1
60
=
4
60
=
1
15

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