Time and work
Time and work
It is one of the easiest topic in quant section. This topic is can fetch you marks
easily but you need to know the right concepts and types of questions to
practice.
We need
to understand relation among time, work done and number of employees working. Since efficiency of different person is different. We discussed
all such problem under the heading of “time and work”.
Here we are explaining two method to solve time and
work question one in basic method and other LCM method .so my point is that you
follow both the method which one is easy for you .but I want to told about LCM
method if your concept are clear properly then you follow LCM method otherwise
you follow basic method it is also easy method. According to me you follow best
to basic method.
1.
Lets
a person do a piece of work in x days. Then
person one day’s work=1/x
2.
Person
one day’s work=1/x, then person can finish the work in x days.
3.
A
can finish 1/x part of work in a day and
B can finish 1/y part of work in day.
If
both will be working together to finish
the task then in a day they can finish
1/x+1/y=x+y/xy
work in one day
part
of the work so to finish the work it require
xy/x+y
days.
Q1. If A can do a work in 8 day, B can do
the same work in 12 days. How many days are required to finish the task if both
are working together ?
Basic method
A’s 1 day’s work =
1/8
B’s 1 day’s work =
1/12
(A+B)’s 1 day’s
work=1/8+1/12=20/8*12=5/24 part of work
So the whole task
finished in 24/5 days. i.e. 4.8days
LCM method
Notes :- Time=total work/efficiency
A+B’s day=24/5=4.8
days
Q2. If
A can do a work in 4 day, B can do the same work in 5 days and C can do the
same work in 10 days. Find the time
taken by A, B and C to do same work in together.
Basic method
A’s 1 day’s work =
1/4
B’s 1 day’s work =
1/5
C’s 1 day’s work =
1/10
(A+B+C)’s 1 day’s
work=1/4+1/5+1/10==11/20 part of work
So the whole task
finished in 20/11 days. i.e. 1.8181days
LCM method
(A+B+C)’s days of
work= 20/11=1.8181 days.
2. When A and B work in alternate days
Case 1:
Starting from A
Lets A can finish the
in 8 days and B can finish the task in 10 days. How many days required to
finish the task if both are working alternate days?
Solution :
A’s 1 day’s work =
1/8 part
A’s 1 day’s work =
1/10 part
Both are working
alternately starting from A
Then in first two
days they can finish 1/8+1/10
8+10/80=18/10
If they continue in
such a manner together in 8 days they can finish 72/80 part of work
Remaining part- 8/80=1/10
Finished by A in 9th
day so. To finish 1/10 part
A need
1/10*8/1=4/5days.
So, together they can
finish the task in 8and 4/5days
In the above question
calculate number of days required to finish the task by A and B if both are
working alternately starting from B
Solution:
Work still remain
same has to finished by B.
(If they start
working alternately starting from B, then on 9th day it will be B’s
turn)
B can finish 1/10part
of the work in 1/10*10/1=1 days
So, together they can
complete the task in 9th days.
LCM method
Case 1.
Starting from A
Efficiency day total work
10 A 8
80
8
B 10
(A+B)’s days of work=
80/18
If they continue in
such a manner together in 8 days they can finish 72/80 part of work
Remaining part- 8/80=1/10
Finished by A in 9th
day so. To finish 1/10 part
A need
1/10*8/1=4/5days.
So, together they can
finish the task in 8and 4/5days
Same like B.
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