A and B together can complete a piece of work in 15 days. B and C together can do it in 24 days. If A is twice as good a workman as C, then in how many days can B alone complete the work?

Let the total work = W

Given, A is twice as good a workman as C

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

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

Let the number of days required for B alone to complete the work = b

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

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

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

A and B together can complete a piece of work in 15 days

$$\Rightarrow$$  Work done by A and B together in 1 day = $$\frac{W}{15}$$

$$\Rightarrow$$  $$\frac{W}{a}$$ + $$\frac{W}{b}$$ = $$\frac{W}{15}$$

$$\Rightarrow$$  $$\frac{1}{a}$$ = $$\frac{1}{15}$$ - $$\frac{1}{b}$$ ............(1)

B and C together can complete the work in 24 days

$$\Rightarrow$$  Work done by B and C together in 1 day = $$\frac{W}{24}$$

$$\Rightarrow$$  $$\frac{W}{b}$$ + $$\frac{W}{2a}$$ = $$\frac{W}{24}$$

$$\Rightarrow$$  $$\frac{1}{b}$$ + $$\frac{1}{2a}$$ = $$\frac{1}{24}$$

$$\Rightarrow$$  $$\frac{1}{b}$$ + $$\frac{1}{2}\left[\frac{1}{15}-\frac{1}{b}\right]$$ = $$\frac{1}{24}$$   [From (1)]

$$\Rightarrow$$  $$\frac{1}{2b}$$ = $$\frac{1}{24}$$ - $$\frac{1}{30}$$

$$\Rightarrow$$  $$\frac{1}{2b}$$ = $$\frac{5-4}{120}$$

$$\Rightarrow$$  $$\frac{1}{b}$$ = $$\frac{1}{60}$$

$$\Rightarrow$$  b = 60

$$\therefore\ $$Number of days required for B alone to complete the work = 60 days

Hence, the correct answer is Option A