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 to...........

Quant (SSC) Time and work

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 same work, If all three, working together can complete the job in 24 days, then the number of days, A alone will take to finish the job is:

100

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Explanation:

Time taken by A : Time taken by B and C together = 3 : 1
Therefore, 1 day's work done by A : 1 day's work done by B and C together = 1 : 3
[Because work done or efficiency is inversely proportional to time taken.]
We can further write the equation as
1 day's work done by A : 1 day's work done by A, B and C together = 1 : 4
Therefore, time taken by A : Time taken by A, B and C together = 4 : 1
Here we can observe that if A, B and C working together takes 1 day,
A alone is taking 4 days which means he is taking 4 times the time taken by A, B and C together.
Therefore, actual time taken by A alone = 4 × 24 = 96 days