A is twice as good a workman as B, and together they finish a piece of work in 13 days. In how many days will A alone finish the work?

$19 \frac{1}{2}$

Given,

A is twice as good a workman as B,

Therefore A : B = 2 : 1 (Efficiency)

⇒ A + B worked for 13 days = (2 + 1) x 13 = 39 units  ..(Efficiency × Days = Total work)

⇒ Time required for A to complete total work alone = \(\frac{39}{2}\) = \( {19 }_{ 2}^{ 1} \) days.   ..(\(\frac{Work}{Efficiency}\) = Time)