A alone can do a piece of work in 10 days. B alone can do the same work in 12 days. They work on alternate days starting with A. In how many days will they complete $\frac{3}{4}$ of the total work?

$\frac{49}{6}$ days

A = 10 days, B = 12 days,

⇒ A + B work on alternate days, starting with A,

 1st day = 6 units,

 2nd day = 5 units,

Every 2 days, 11 units are done,

So, in 8 days, 44 units are done,

⇒ \(\frac{3}{4}\) of total work = \(\frac{3}{4}\) x 60 = 45 units,

So, in \( { 8}_{6 }^{1 } \) = \(\frac{49}{6}\) days, 45 units of work is completed,