Question

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?​

Answer 1

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 .