Working together A and B can complete a work in 12 days. They work together for 9 days after which B leaves. If A finishes the remaining work in 5 days, then the number of days that B alone would take to complete the work is:

Let's assume the total work is 60 units.

Working together A and B can complete a work in 12 days.

The efficiency of A and B together = $$\frac{60}{12}$$ = 5 units/day

They work together for 9 days after which B leaves. If A finishes the remaining work in 5 days.

$$9\times5+5\times efficiency\ of\ A=60$$

$$45+5\times\ efficiency\ of\ A=60$$

$$5\times\ efficiency\ of\ A= 60-45 = 15$$

the efficiency of A = 3 units/day

the efficiency of B = 5-3 = 2 units/day

The number of days B alone would take to complete the work is = $$\frac{60}{2}$$

= 30 days