There is a group of persons each of whom can complete a piece of work in 16 days, when they are working individually. On the first day one person works, on the second day another person joins him, on the third day one more person joins them and this process continues till the work is completed. How many days are needed to complete the work?  Select the correct option.
A) 3 1⁄4 days  B) 4 1⁄3 days  C) 5 1⁄6 days  D) 6 1⁄5 days  E) 7 1⁄5 days
Explanation :   Work completed in 1st day = 1/16   Work completed in 2nd day = (1/16) + (1/16) = 2/16   Work completed in 3rd day = (1/16) + (1/16) + (1/16) = 3/16   …   An easy way to attack such problems is from the choices. You can see the choices are   very close to each other. So just see one by one.   For instance, The first choice given in 3 1⁄4   The work done in 3 days = 1/16 + 2/16 + 3/16 = (1+2+3)/16 = 6/16   The work done in 4 days = (1+2+3+4)/16 = 10/16   The work done in 5 days = (1+2+3+4+5)/16 = 15/16, almost close, isn't it?   The work done in 6 days = (1+2+3+4+5+6)/16 &gt; 1   Hence the answer is less than 6, but greater than 5. Hence the answer is 5 1⁄6 days.   (Just for your reference, work done in 5 days = 15/16.   Pending work in 6th day = 1 – 15/16 = 1/16.   In 6th day, 6 people are working and work done = 6/16.   To complete the work 1/16, time required = (1/16) / (6/16) = 1/6 days.   Hence total time required = 5 + 1/6 = 5 1⁄6 days   Answer : Option 5 1⁄6 days
<result>C</result>
There is a group of persons each of whom can complete a piece of work in 16 days, when they are working individually. On the first day one person works, on the second day another person joins him, on the third day one more person joins them and this process continues till the work is completed. How many days are needed to complete the work?