Time & Work more Questions with their tricky conceptual solutions continues...................
More types of questions will be followed soon on this blog........................
Type 2nd :- Questions based One day work Concept:-
In these
type of questions you just have to read the questions carefully to analyse the
given data in the question and then calculate the required answer with the help
of one day work concept or formula given in this post, which ever you feel more
comfortable to solve the question.
Q12. A, B and C can do a work in 8 days,
16 days and 24 days respectively. They all began to do the same work together.
A continuous with the work till the end of the work while C left the work
before 2 days and B left the work 1 day before the work got completed.
Calculate in how many days does the work got completed.
Solution:- First of all you should read this
question carefully and analyse it carefully in such manner:-
Method 1st :- The work in this question is same
means it is constant and always be considered as 1 (one) work only.
Let the
work got completed in “x” days
worker “A”
can do a piece of work in “8 days”
Therefore
the one day work of worker “A” = (1/8) work
According
to question “A” worked till the end therefore total work done by “A” = (x/8).
worker “B”
can do a piece of work in “16 days”
Hence the
one day work of worker “B” = (1/16) work
“B” worked
only till 1 day before therefore total work done by “B” = {(x – 1)/16}.
worker “C”
can do a piece of work in “24 days”
Hence the
one day work of worker “C” = (1/24) work
“C” worked
only till 2 days before therefore total work done by “C” = {(x – 2)/24}
Now we know
that;
Total work done by “A” + Total work
done by “B” + Total work done by “C” = 1 (Total work).
(x/8) + {(x – 1)/16} + {(x – 2)/24} = 1
Taking LCM
(48) and Solving we get,
[6x + 3(x -
1) + 2(x - 2)]/48 =1
6x + 3x – 3
+ 2x – 4 = 48
11x – 7 = 48
11x = 55
x = 5 days.
Hence the work got completed in 5 days.
Q13. A is thrice as fast as B and A can
do a work in 60 days less than B. Find the number of days in which they can do
the same work, working together?
Sol. The work in this question is same
means it is constant and always be considered as 1 (one) work only.
Worker A B
Efficiency 3x x
In these
questions the frequencies are interchanged to get the number of days of
respective workers. Therefore the number of days in which workers “A” and “B”
can do the same worker in following number of days.
No. of
days x 3x
According
to the question worker “B” completes the same work in 60 days less.
Therefore,
difference between the number of days taken by the workers = 60.
No. of days
taken by “B” alone to do the same work – No. of days taken by “A” alone to do
the same work = 60
3x – x =
60.
2x = 60.
x = 60/2 =
30 days.
Hence the
worker “A” can do the same work in x days = 30 days.
The one day
work of worker “A” = (1/30) work.
The worker
“B” can do the same work in 3x days = 3 × 30 = 90 days.
The one day
work of worker “B” = (1/90) work.
The one day
work done by workers “A” and “B” together = (1/30) + (1/90)
= {(3 +
1)/90} work.
= (4/90)
work.
Now number
of days taken by workers “A” and “B” together to do the same work = total work
/ one day work of workers “A” and “B” together.
Number of
days = {1/(4/90)} days.
Number of
days = (45/2) days = 22.5 days.
OR
Number of
days taken by workers “A” and “B” together to complete the work
= (D1 ×
D2)/( D1 + D2) = (30 × 90)/ (30 + 90)
= (30 ×
90)/120 = (90/4) days.
= 22.5
days.
Hence the workers “A” and “B” can do the same
work in 22.5 days.
(Note you may say that this is so
long but dear this is the only way to explain the whole concept of the question
to you now its upto you that how fast and short handedly you can solve these
type of questions)
The Various
Questions related to this and other concept which are frequently asked in the
examinations will be presented to your for self study on this blog soon, so
keep visiting and sending your suggestions and requirements too to us through
the forum.
More types of questions will be followed soon on this blog........................
No comments:
Post a Comment