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A can finish a job in 20 days while B can finish same job in 30 days. A and B both worked for 5 days and C joins them. In next 3.5 days, all three have manage to complete the job. Find in how many days C alone can finish the job.

A can finish a job in 20 days while B can finish same job in 30 days. A and B both worked for 5 days and C joins them. In next 3.5 days, all three have manage to complete the job. Find in how many days C alone can finish the job. Correct Answer 12 days

Given,

A's 1 day's work = 1/20

B's 1 day's work = 1/30

(A + B)’s 1 day's work = 1/20 + 1/30 = 1/12

(A + B)’s 5 day's work = 5/12

Remaining fraction of work after 5 days = 1 – 5/12 = 7/12

Let C's 1 day's work be 1/M.

Then,

⇒ (1/12 + 1/M) = 7/12 × 1/3.5

⇒ (1/12 + 1/M) = 1/6

⇒ 1/M = 1/12

C alone can complete the work in 12 days.

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