A man takes 16 days to complete a project. A woman does the same work in 12 days. They started the work together on alternate days and the man worked on the first day. How much time will they take to complete the work?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 55/4 days
Concept Used :
Total Work = Efficiency × Time
Given that, Man can do the work in 16 days
And women can do it in 12 days
Let the total work to be done be LCM of (16, 12) = 48 units
Efficiency of a man = 48/16 = 3 units/day
Efficiency of a woman = 48/12 = 4 units/day
They work alternatively, So the work completed in 2 days = 7 units
Similarily work done in 12 days = 42 units
Now remaining work = 48 - 42 = 6 units
Now a man works for 1 day, the amount of work done = 3 units
Now, remaining work = 3 units
So, the time required by a woman to complete 3 units of work = 3/4 days
So, the total number of days to complete the work = 13 + 3/4 = 55/4.
Hence the required time to complete the work is 55/4 days.