A and B can complete a certain work in 6 days and 8 days, respectively. They worked together for 3 days. C alone completed the remaining work in 2 days. B and C together can complete $\frac{3}{4}$ of the same work in:

4 days

A = 6 days, B = 8 days,

⇒ A + B worked for 3 days = (4 + 3) x 3 = 7 x 3 = 21 units,

⇒ Remaining work = 24 - 21 = 3,

⇒ Remaining work completed by C in 2 days = \(\frac{3}{C}\) = 2 days,

⇒ C =  \(\frac{3}{2}\), (Efficiency) 

⇒ \(\frac{3}{4}\) of total work = \(\frac{3}{4}\) x 24 = 18 units,

⇒ Time required by B + C to complete 18 units of work = \(\frac{18}{3+3/2}\) = \(\frac{18}{9/2}\) = 4 days,    ..(\(\frac{Work}{Efficiency}\) = Time)