Question 109

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

Let time taken by B and C = $$x$$ days

=> Time taken by A = $$3x$$ days

Thus, part of work done by A, B & C in 1 day

= $$\frac{1}{x} + \frac{1}{3x} = \frac{4}{3x}$$

Acc to ques :

=> $$\frac{4}{3x} = \frac{1}{24}$$

=> $$x = \frac{4\times24}{3} = 32$$ days

=> Time taken by A alone = 32*3 = 96 days

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