A man can complete a work in 20 days, and a woman can complete the same work in 10 days. If they work on it together for 5 days, then how many days will the woman take to complete the rest of the work?

$2\frac{1}{2}$

Man = 20 days,

Women = 10 days,

⇒ M + W worked for 5 days = (1 + 2) x 5 = 15 units  ..(Efficiency × Days = Total work)

⇒ Remaining units = 20 - 15 = 5 units.

⇒ Time taken by woman to complete the 5 units = \(\frac{5}{2}\) = \( { 2}_{ 2}^{ 1} \) days.      ..(\(\frac{Work}{Efficiency}\) = Time)