A takes three times as long as B and C together to do a job. B takes four times as long as A and C together to do the work. If all the three, working together can complete the job in 24 days, then the number of days, A alone will take to finish the job is = ?

Answer: Option B

Let time taken by B and C = x days
∴ Time taken by A = 3x days
∴ Part of work done by A, B and C in 1 day
$$\begin{array}{rl}& =\frac{1}{\text{x}}+\frac{1}{3\text{x}}=\frac{3+1}{3\text{x}}=\frac{4}{3\text{x}}\\ & \therefore \frac{4}{3\text{x}}=\frac{1}{24}\\ & \Rightarrow 3\text{x}=4\times 24\\ & \Rightarrow \text{x}=\frac{4\times 24}{3}=32\text{days}\end{array}$$
∴ Time taken by A = 32 × 3 = 96 days.

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Alternet :
Work done by all of them together in $$\frac{1}{24}$$
Efficiency of A : Efficiency of (B + C) = 1 : 3
Work done by A in 1 day = $$\frac{1}{24}$$ × $$\frac{1}{4}$$ = $$\frac{1}{96}$$
i.e., A alone can finish the job in 96 days.

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Alternet :
Suppose A can complete the job in 3x days and (B + C) can complete the job in x days.
$$\begin{array}{rl}& \frac{3\text{x}\times \text{x}}{3\text{x}+\text{x}}=24\\ & \Rightarrow \frac{3\text{x}}{4}=24\\ & \Rightarrow \text{x}=32\\ & 3\text{x}=96\text{days.}\end{array}$$