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

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

Step 1
How to approach work time questions?

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

Understanding relation between time taken and rate
· If A takes ‘a’ days to complete a task
01

· If A takes ‘a’ days to complete a task A will complete
1
a
of the task in a day
01

1
a
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

1
a
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

Understanding relation between time taken and rate. Continued….01

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

  The correct expression is
1
a +
1
b =
1
10
01

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.
  The correct expression is
1
a +
1
b =
1
10
01

Step 2
Frame equation; solve equation

· Working alone, let A take ‘a’ days to complete the
task.

task.
A will complete
1
a
of the task in a day.

task.
A will complete
1
a
· Working alone, B take 60 days to complete the
task.

task.
A will complete
1
a
task.
B will complete
1
60

task.
A will complete
1
a
task.
B will complete
1
60
· Working together A and B will complete
1
a
+
1
60
of
the task in a day.

task.
A will complete
1
a
task.
B will complete
1
60
1
a
+
1
60
of
the task in a day.
Working together A and B take 12 days.

task.
A will complete
1
a
task.
B will complete
1
60
1
a
+
1
60
of
the task in a day.
 they complete
1
12
of the task in a day .

task.
A will complete
1
a
task.
B will complete
1
60
1
a
+
1
60
of
the task in a day.
·
 they complete
1
12
Equating the two,
1
a
+
1
60
=
1
12

task.
A will complete
1
a
task.
B will complete
1
60
1
a
+
1
60
of
the task in a day.
·
 they complete
1
12
Equating the two,
1
a
+
1
60
=
1
12 Or
1
a
=
1
12
-
1
60

task.
A will complete
1
a
task.
B will complete
1
60
1
a
+
1
60
of
the task in a day.
·
 they complete
1
12
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

A takes 15 days
task.
A will complete
1
a
task.
B will complete
1
60
1
a
+
1
60
of
the task in a day.
·
 they complete
1
12
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

Correct Answer : Choice E
A takes 15 days
task.
A will complete
1
a
task.
B will complete
1
60
1
a
+
1
60
of
the task in a day.
·
 they complete
1
12
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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4GMAT Diagnostic Test Q18 - Word Problem - Rates - Work Time

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