A can complete a certain work in 30 days. He started the work. After 4 days, B joined him and the whole work was completed in 10 days from the beginning. B alone can complete one-third of the same work in:

3 days

A = 30 days,

Lets' take A's efficiency as 1,

Therefore, total work = 1 x 30 = 30 units,   ..(Efficiency × Days = Total work)

⇒ A worked for 4 days = 1 x 4 = 4 units,

⇒ Remaining work = 30 - 4 = 26 units,

⇒ B joined A and they complete 26 units in 6 days = \(\frac{26}{1+B}\) = 6 days,

⇒ B = \(\frac{10}{3}\)  (Efficiency)

⇒ Time required by b to complete \(\frac{1}{3}\)rd of the work = \(\frac{1}{3}\) x 30 = \(\frac{10}{10/3}\) = 3 days,   ..(\(\frac{Work}{Efficiency}\) = Time)