In the
previous post of Time and work we discussed about some questions of basic
concepts of this chapter. Now we will see some of the some more various
frequently asked important question of this chapter in competition like SSC,
Bank (IBPS), and Railways. This chapter is one of the easiest chapters for
students to solve with less calculations.
Type 3rd :- Questions
based One day work Concept with Efficiency:-
Q14. A is twice as good as workman B.
Together they can do a work in 14 days. In how many days can it be done by each
separately?
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 2x 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 2x
One day
work (1/x) (1/2x)
According
to the question workers “A” and “B” can complete a work together in 14 days.
Therefore,
the one day work done by “A” and “B” together = (1/14) work.
Now
applying one day work concept:-
(1/x) +
(1/2x) = (1/14)
Taking LCM
and solving we get,
(3/2x) =
1/14.
x = 21
Hence the
no. of days taken by worker “A” to complete the same work alone = x = 21 days.
And the no.
of days taken by worker “B” to complete the same work alone = 2x = 2 × 21
= 42days.
Hence “A”
and “B” can do the same work in 21 days and 42 days respectively alone.
OR
Number of
days taken by workers “A” and “B” together to complete the work = D = 14 days
As assumed
“A” can do the same work in D1 = x days.
And “B” can
do the same work in D2 = 2x days.
Now Using
formula:-
D = (D1
× D2)/( D1 + D2) = (x × 2x)/ (x + 2x)
Putting the
values,
14 = (2x2)/(3x)
14 =
(2x/3).
x = (14 ×
3)/2 = 21 days (No. of days taken by “A” alone.)
And no. of
days taken by worker “B” to complete the same work alone = 2x = 2 × 21
= 42days.
Hence “A” and “B” can do the same work in 21 days
and 42 days respectively alone.
Q15. “A” is thrice as fast as “B” and together
they can complete a work in 15 days. In how many days will B take to complete
the same work alone?
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
One day
work (1/x) (1/3x)
According
to the question workers “A” and “B” can complete a work together in 15 days.
Therefore,
the one day work done by “A” and “B” together = (1/15) work.
Now
applying one day work concept:-
(1/x) +
(1/3x) = (1/15)
Taking LCM
and solving we get,
(4/3x) = 1/15.
x = 20
Hence the
no. of days taken by worker “B” to complete the same work alone = 3x = 3 × 20
= 60days.
Hence “B” can do the same work in 60
days alone.
OR
Number of
days taken by workers “A” and “B” together to complete the work = D = 15 days
As assumed
“A” can do the same work in D1 = x days.
And “B” can
do the same work in D2 = 3x days.
Now Using
formula:-
D = (D1
× D2)/( D1 + D2) = (x × 3x)/ (x + 3x)
Putting the
values,
15 = (3x2)/(4x)
15 =
(3x/4).
x = (15 ×
4)/3. = 20 days (No. of days taken by “A” alone.)
And no. of
days taken by worker “B” to complete the same work alone = 3x = 3 × 20
= 60 days.
Hence “B” can do the same work in 60
days alone in 60 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........................
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