AMCAT Time and Work Quiz-1

Solution:
Time taken by three of them =1.5hrs = 90 minutes
Time taken by Aman and Rahul = 2.5 hrs = 150 minutes
Time is taken by Aryan to do the task =
1/90 – 1/150
= 2/450
= 225 minutes

Solution:
6 women take time to do the task =
8 * 12 = 6 * days
Days = 16
When 4 men do the same work in 16 days
Therefore, their one day’s work = 1/16
When 6 women do the work in 16 days
One day’s work by 6 women = 1/16
Hence, the time required by 4 engineers and 6 labors to do the same work =
= 1/16 + 1/16
= 8 days

Let us assume the two cooler as X and Y
X cools at 20 minutes
Y at 25 minutes
Together = (X * Y)/(X + Y)
= (20 * 25)/(20 + 25)
= 25 * 20/45
= 500/45
= 11.1 minutes.

Solution:
Taylor’s 9 day’s project = 1/ 18 * 9
=\frac{1}{2}
Now, when Robert does the remaining project,
=1-\frac{1}{2}

=\frac{1}{2}
The time needed by Robert to do the project
= \frac{1}{16}\times2
= \frac{1}{8}
= 8 days

Solution:
Number of minutes =
30 * 60 = 56 * minutes
Minutes = 36

Solution:
25 woman can do an assignment in 15 days
So, the number of women needed to do the work = 25 * 15 = women * 5
= 75

Solution:
Men x hour = Men x s
7 x 35 = 49 x s
S =245/49
= 5 hours

 

Solution:
Work done by V in one day = \frac{1}{7}
Work done by W in one day = \frac{1}{14}
Work done by X in one day = \frac{1}{21}
Therefore, together they need \frac{1}{7} +\frac{1}{14} + \frac{1}{21}
= \frac{11}{42}
Or \frac{42}{11} days

Solution:
One day’s work by a boy = x
One day’s work by a girl = y
Therefore,
4x + 6y = \frac{1}{8}
3x + 7y = \frac{1}{10}
Solving both these equations, we get
Y =\frac{1}{400}, and x = \frac{11}{400}
Therefore, one girl’s day’s work =\frac{1}{400}
Therefore, 10 girl’s day’s work = 1 x \frac{10}{400}
=\frac{1}{40}
Thus, 10 girls can do the same work in 40 days.

Solution:
Work done by Sameer = 3 x 12 = 36 hours
Work done by Mayur = 3 x 8 = 24 hours
Work done by Sameer in one hour = \frac{1}{36}
Work done by Mayur in one hour = \frac{1}{24}
Work done together = \frac{1}{36}+\frac{1}{24}
= \frac{5}{72} hours
Or,
\frac{72}{5}\times\frac{5}{12}
= 6 days