A can do a piece of work in 30 days. He completed 40% of the work and then left. B completed the remaining work in 21 days. Working together, A and B will complete 65% of the same work in:

$10\frac{1}{2}$ days

A = 30 days,

Take efficiency of A as 1,

Total work = 1 x 30 = 30 units,

A did 40% of the work and left = 40% of 30 = 12 units,

Remaining work = 30 - 12 = 18 units,

⇒ B complete 18 units in 21 days = \(\frac{18}{21}\) = \(\frac{6}{7}\) (Efficiency of B)

⇒ Time required by A + B to complete 65% of the total work i.e; 19.5 units of work = \(\frac{19.5}{1+6/7}\) = \(\frac{21}{2}\) = \( {10 }_{ 2}^{1 } \) days,    ..(\(\frac{Work}{Efficiency}\) = Time)