Arshi can do a piece of work in 30 days, while Ahan can complete it in 20 days. Both together work for 4 days and afterward Ahan leaves. How long will Arshi take to complete the remaining work?

Let's assume the total work is 60 units.

Arshi can do a piece of work in 30 days.

Efficiency of Arshi = $$\frac{60}{30}$$ = 2 units/day

Ahan can complete it in 20 days.

Efficiency of Ahan = $$\frac{60}{20}$$ = 3 units/day
Both together work for 4 days and afterward Ahan leaves. So let's assume the time taken by Arshi to complete the remaining work is 'y' days.

4$$\times$$(Efficiency of Arshi and Ahan) + y $$\times$$(Efficiency of Arshi) = 60

$$4\times(2+3) + y \times2 = 60$$

$$4\times5 + 2y = 60$$

20 + 2y = 60

2y = 60 - 20

2y = 40

y = 20

So the time taken by Arshi to complete the remaining work is 20 days.