Question

If q workers can paint a house in d days, how many days will it take q+2 workers to paint the same house, assuming all workers paint at the same rate ?A. d+2B. d-2C. q+2 / qdD. qd / q+2E. (qd + 2d) / q

Answer 1

Answer: D.
`(qd)/((q+2))`

Explanation:

Given : q workers can paint a house in d days.

Let
`d_1` 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 :
`x_1y_1=x_2y_2`

Substitute ,
`x_1=q ,\ y_1=d` and
`x_2=q+2 ,\ y_2=d_2` , we get

`qd=(q+2)d_2\\\\\Rightarrow\ d_2=(qd)/((q+2))`

Therefore , the number of days it will take q+2 workers to paint the same house =
`(qd)/((q+2))`

Hence, the correct answer is : D.
`(qd)/((q+2))`