P is two times more efficient than Q. P is able to complete a piece of work in 40 days less than Q. Working together, the whole number of days taken by them to complete the work is: (Round off to the nearest integer)

Let the work done by Q in one day be ( x ). Then, the work done by P in one day is ( 2x ).

Let the number of days taken by Q to complete the work be ( d ). Therefore, the time taken by P to complete the work is ( d – 40 ).

Since work is equal to the rate of work multiplied by the time taken, we can equate the total work done by both:

[

Q’s work = x cdot d

]

[

P’s work = 2x cdot (d – 40)

]

Since both complete the same piece of work, we have:

[

x cdot d = 2x cdot (d – 40)

]

Dividing both sides by ( x ) (assuming ( x neq 0 )) gives:

[

d = 2(d – 40)

]

Expanding and solving for ( d ):

[

d = 2d – 80

]

[

80 = d

]

Now that we have ( d ), the number of days Q takes to complete the work is 80 days. The number of days P takes is:

[

d – 40 = 80 – 40 = 40 text{ days}

]

Next, we can find the rate of work for Q (in terms of total work done):