A is twice as good a workman as B and together they finish a piece of work in 22 days. In how many days will A alone finish the same work?

Let the total work = W

A is twice as good a workman as B

Let the number of days required for A alone to complete the work = a

$$\Rightarrow$$ Number of days required for B alone to complete the work = 2a

Work done by A in 1 day = $$\frac{W}{a}$$

Work done by B in 1 day = $$\frac{W}{2a}$$

Given, A and B together finish the work in 22 days

$$\Rightarrow$$  Work done by A and B together in 1 day = $$\frac{W}{22}$$

$$\Rightarrow$$  $$\frac{W}{a}$$ + $$\frac{W}{2a}$$ = $$\frac{W}{22}$$

$$\Rightarrow$$  $$\frac{3}{2a}$$ = $$\frac{1}{22}$$

$$\Rightarrow$$   a = 33

$$\therefore\ $$Number of days required for A alone to complete the work = 33 days

Hence, the correct answer is Option C