P is two times 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)

Correct option is C

Given:
P is two times more efficient than Q, and P completes the work in 40 days less than Q.
Solution:
Let Q's time to complete the work be x days
Then, P's time = x - 40 days
Efficiency of P : Efficiency of Q= 2:1
Q's work in one day = 1/x
P's work in one day = 2/x
​$$\frac2x × (x - 40) = 1$$​​
2(x - 40) = x
2x - 80 = x
x = 80
P's time = 80 - 40 = 40 days
Combined work per day =$$\frac1{80} + \frac1{40} = \frac{(1 + 2)}{80} = \frac{3}{80}$$​​
Days taken together =$$\frac {80}{3} ≈ 27$$ days

Alternate Method:
Efficiency of P:Q=2:1 (2-1) unit → 40 days. 1 unit =40 days Time of P:Q=1:2

Required time =80/3 =26.67 days or =27 days.