A alone can do a piece of work in 12 days. B alone can do the same work in 18 days. C alone can do the same work in 24 days. In how many days will they complete 65% of the work, if all three work together?

Let's assume the total work is 72 units.

A alone can do a piece of work in 12 days.

Efficiency of A = $$\frac{72}{12}$$ = 6 units/day

B alone can do the same work in 18 days.

Efficiency of B = $$\frac{72}{18}$$ = 4 units/day

C alone can do the same work in 24 days.

Efficiency of C = $$\frac{72}{24}$$ = 3 units/day

Time taken by all three working together to complete 65% of the work = 65% of $$\frac{72}{\left(6+4+3\right)}$$

= 65% of $$\frac{72}{13}$$

= $$\frac{65}{100}\times\frac{72}{13}$$

= $$\frac{5}{100}\times72$$

= $$\frac{360}{100}$$

= 3.6 days