A husband and wife, started painting their house, but husband left painting 5 days before the completion of the work. How many days will it take to complete the work, which the husband alone would have completed in 20 days and wife in 15 days?
HUSBAND takes 20 days to complete one unit of work
So , H take 20 days = 1
W take 15 days = 1
H one day work = 1/20 and W one day work = 1/15
H + W one day work = 1/20 + 1/15 = 7/60.
Since husband left painting 5 days before the completion of the work.
In a total of X day H+W worked for X-5 and W alone for 5
(7/60) (X-5) + 1/15 * 5 = 1 therefore X = 75/7
Hence the answer is option C