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 = ?

Solution(By Examveda Team)

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
$$\eqalign{ & = \frac{1}{{\text{x}}} + \frac{1}{{3{\text{x}}}} = \frac{{3 + 1}}{{3{\text{x}}}} = \frac{4}{{3{\text{x}}}} \cr & \therefore \frac{4}{{3{\text{x}}}} = \frac{1}{{24}} \cr & \Rightarrow 3{\text{x}} = 4 \times 24 \cr & \Rightarrow {\text{x}} = \frac{{4 \times 24}}{3} = 32\,{\text{days}} \cr} $$
∴ 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.
$$\eqalign{ & \frac{{3{\text{x}} \times {\text{x}}}}{{3{\text{x}} + {\text{x}}}} = 24 \cr & \Rightarrow \frac{{3{\text{x}}}}{4} = 24 \cr & \Rightarrow {\text{x}} = 32 \cr & 3{\text{x}} = 96\,{\text{days.}} \cr} $$