A, B, C can individually complete a work in 20 days, 15 days, 12 days respectively. B and C start the work and they worked for 3 days and left. Then the number of days required by A to finish the remaining work is

Solution

A, B, C can individually complete a work in 20 days, 15 days, 12 days respectively

Efficiency of (A + B + C) = $$\left(\frac{1}{20}+\frac{1}{15}\ +\frac{1}{12}\right)$$ = $$\left(\frac{3+4+5}{60}\right)\ =\ \frac{12}{60\ }$$

Efficiency of only (B + C) =$$\left(\frac{1}{15}+\frac{1}{12}\right)$$ = $$\left(\frac{4+5}{60}\right)\ = \ \frac{9}{60\ }$$

So efficiency of A = $$\frac{12}{60}-\frac{9}{60}\ =\ \frac{3}{60}$$

While working, all 3 work for 3 days.

So work completed in 3 days = $$3\ \times\ \frac{12}{60}\ =\ \frac{36}{60}$$

Work Remaining = $$1\ -\frac{36}{60}\ =\ \frac{24}{60}$$ 

If A works alone @ $$\frac{3}{60}$$ work per day. = $$\frac{\left(\frac{24}{60}\right)}{\left(\frac{3}{60}\right)}$$ = 8 days.