Ajay, Raman and Bhaskar together can complete a piece of work in 3 days. Ajay takes 3 days more than
Raman to complete the same piece of work alone and Raman takes 1/31d the time that Bhaskar takes to
complete the same work alone. In how many days Bhaskar alone, can complete the same piece of work?
Answers
18 days
Step-by-step explanation:
Correction : 1/3rd not 1/31d
Given :-
Ajay, Raman and Bhaskar together can complete a piece of work in 3 days. Ajay takes 3 days more than Raman to complete the same piece of work alone and Raman takes 1/3rd the time that Bhaskar takes to complete the same work alone.
To find :-
In how many days Bhaskar alone, can complete the same piece of work?
Solution :-
Given that:-
Ajay, Raman and Bhaskar together can complete a piece of work in 3 days.
( For convenience Ajay = A , Raman = R , Bhaskar = B )
So, The work completed by three people in one day = 1/3rd of the work.
A+R+B = 1/3 -----------(1)
Let the work completed by Bhaskar be in X days
The part of the work completed by Bhaskar in one day = (1/X)
B = 1/X -----------(2)
Now,
The work completed by Raman = 1/3rd of the time that Bhaskar alone
=> The work completed by Raman in (1/3) of (X)
=> X/3
The work completed by Raman in one day =
1/(X/3)
=> 3/X
R = 3/X --------------(3)
and
Ajay takes 3 days more than Raman to complete the same piece of work alone.
The work completed by Ajay = Raman's working days +3
=> (X/3)+3
=> (X+9)/3
The work completed by Ajay in one day =
=> 1/[(X+9)/3]
A = 3/(X+9) ------------(4)
Total work completed by the three people in one day
From (2),(3)&(4)
=> A+R+B
=> [3/(X+9)] +(3/X) +(1/X)
=>[3/(X+9)] +[(3+1)/X]
=> [3/(X+9)] +(4/X)
LCM of (X+9) and X = X(X+9)
=> [(3×X)+(4×(X+9))]/[X(X+9)]
=> (3X+4X+36)/(X(X+9))
=> (7X+36)/(X²+9X) -------------(5)
(1) and (5) are same
=> (7X+36)/(X²+9X) = 1/3
On applying cross multiplication then
=> 3(7X+36) = 1(X²+9X)
=> 21X+108 = X²+9X
=> X²+9X-21X-108 = 0
=> X²-12X-108 = 0
=> X²-18X+6X -108 = 0
=> X(X-18) +6(X-18) = 0
=> (X-18)(X+6) = 0
=> X-18 = 0 or X+6 = 0
=> X = 18 or X = -6
X can not be negative.
So, X = 18
Therefore, X = 18 days
Answer:-
In 18 days Bhaskar can complete the same piece of work alone .