Answer: D. [tex]\dfrac{qd}{(q+2)}[/tex]
Step-by-step explanation:
Given : q workers can paint a house in d days.
Let [tex]d_1[/tex] be the number of days taken by q+2 workers to paint the same house.
Since there is inverse relationship between the number of workers and the number of days to do same work ( condition - all workers paints at the same rate), as the number of workers increases the number of days to complete it decreases.
Equation of inverse variation between x and y : [tex]x_1y_1=x_2y_2[/tex]
Substitute , [tex]x_1=q ,\ y_1=d[/tex] and [tex]x_2=q+2 ,\ y_2=d_2[/tex] , we get
[tex]qd=(q+2)d_2\\\\\Rightarrow\ d_2=\dfrac{qd}{(q+2)}[/tex]
Therefore , the number of days it will take q+2 workers to paint the same house = [tex]\dfrac{qd}{(q+2)}[/tex]
Hence, the correct answer is : D. [tex]\dfrac{qd}{(q+2)}[/tex]
