A man can finish a piece of work in 15 days. A woman can complete the same work in 10 days. Both work together for 5 days, then the man leaves. How many days will be taken by the woman to finish the remaining work?

$1\frac{2}{3}$

Man = 15 days, Woman = 10 days,

⇒ Man + Woman worked for 5 days = (2 + 3) x 5 = 25 units,  ..(Efficiency × Days = Total work)

⇒ Remaining work = 30 - 25 = 5 units,

⇒ Man left so time required by Woman to complete 5 units of work = \(\frac{5}{3}\) = \( { 1}_{3 }^{2 } \) days,  ..(\(\frac{Work}{Efficiency}\) = Time)