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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 Balone takes 60 days to complete the task, how long will Aalone 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
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 A will complete 1a
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
Understanding relation between time taken and rate
· If A takes ‘a’ days to complete a task A will complete 1a
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
Understanding relation between time taken and rate
· If A takes ‘a’ days to complete a task A will complete 1a
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
120
th of the task and
B will complete 130
th of the task.
Together they will complete 1
20+
130
=3+260
=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
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
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
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 1a
+1b
=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
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 1a
+1b
=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
Step 2
Frame equation; solve equation
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.
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
1a
of the task in a day.
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
1a
of the task in a day.
· Working alone, B take 60 days to complete the
task.
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
1a
of the task in a day.
· Working alone, B take 60 days to complete the
task.B will complete
160
of the task in a day.
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
1a
of the task in a day.
· Working alone, B take 60 days to complete the
task.B will complete
160
of the task in a day.
· Working together A and B will complete 1a
+ 160
of
the task in a day.
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
1a
of the task in a day.
· Working alone, B take 60 days to complete the
task.B will complete
160
of the task in a day.
· Working together A and B will complete 1a
+ 160
of
the task in a day.
Working together A and B take 12 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
1a
of the task in a day.
· Working alone, B take 60 days to complete the
task.B will complete
160
of the task in a day.
· Working together A and B will complete 1a
+ 160
of
the task in a day.
Working together A and B take 12 days.
they complete 112
of the task in a day .
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
1a
of the task in a day.
· Working alone, B take 60 days to complete the
task.B will complete
160
of the task in a day.
· Working together A and B will complete 1a
+ 160
of
the task in a day.
Working together A and B take 12 days.
·
they complete 112
of the task in a day .
Equating the two,1a
+ 160
= 112
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
1a
of the task in a day.
· Working alone, B take 60 days to complete the
task.B will complete
160
of the task in a day.
· Working together A and B will complete 1a
+ 160
of
the task in a day.
Working together A and B take 12 days.
·
they complete 112
of the task in a day .
Equating the two,1a
+ 160
= 112 Or
1a
= 112
-160
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
1a
of the task in a day.
· Working alone, B take 60 days to complete the
task.B will complete
160
of the task in a day.
· Working together A and B will complete 1a
+ 160
of
the task in a day.
Working together A and B take 12 days.
·
they complete 112
of the task in a day .
Equating the two,1a
+ 160
= 112 Or
1a
= 112
-160
1a
= 5 - 160
= 460
= 115
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
1a
of the task in a day.
· Working alone, B take 60 days to complete the
task.B will complete
160
of the task in a day.
· Working together A and B will complete 1a
+ 160
of
the task in a day.
Working together A and B take 12 days.
·
they complete 112
of the task in a day .
Equating the two,1a
+ 160
= 112 Or
1a
= 112
-160
1a
= 5 - 160
= 460
= 115
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
1a
of the task in a day.
· Working alone, B take 60 days to complete the
task.B will complete
160
of the task in a day.
· Working together A and B will complete 1a
+ 160
of
the task in a day.
Working together A and B take 12 days.
·
they complete 112
of the task in a day .
Equating the two,1a
+ 160
= 112 Or
1a
= 112
-160
1a
= 5 - 160
= 460
= 115
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