X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?  Answers
A) 11 B) 10 C) 99 D) 87 E) 55
Work done by X in 4 days = (1/20 * 4) = 1/5   Remaining work = (1 - 1/5) = 4/5   (X + Y)'s 1 day work = (1/20 + 1/12) = 2/15   Now, 2/15 work is done by X and Y in 1 day.   So, 4/5 work will be done by X and Y in (15/2 * 4/5)= 
<gadget id="calculator">(15/2 * 4/5)</gadget>
<output>6</output>
6 days.   Hence, total time taken= (6 + 4)= 
<gadget id="calculator">(6 + 4)</gadget>
<output>10</output>
10 days.   Answer:10
<result>B</result>
X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?