A takes three times as long 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 :

A takes three times as long 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 :
[A]90 days
[B]95 days
[C]96 days
[D]100 days

96 days
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
$latex = \frac{1}{x}+\frac{1}{3x} = \frac{3+1}{3x} = \frac{4}{3x}&s=1$
$latex \therefore \frac{4}{3x} = \frac{1}{24}&s=1$
$latex => 3x = 4\times 24&s=1$
$latex => x = \frac{4\times 24}{3} = 32\ days&s=1$
∴ Time taken by A = 32 $latex \times$ 3 = 96 days.
Hence option [C] is correct answer.


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