# A can do a job in 16 days and B can do the same job in 12 days. With the help of C, they can finish the job in 6 days only. Then, C alone can finish it in (a) 34 days (b) 22 days (c) 36 days (d) 48 days

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Given that A can do a job in 16 days

B can do the same job in 12 days

A and B, with the help of C, can finish the job in 6 days.

We have to find the number of days in which C alone can finish the job.

Time and work problems establish the relationship between the number of persons doing the work, the time taken by the persons to complete the work, and the amount of work done.

Work done = number of person x time taken.

We know that if a piece of work is done in ‘a’ number of days, then the work done in one day = 1/a.

A’s one-day work = 1/16

B’s one-day work = 1/12

A and B’s one-day work = 1/16 + 1/12

= (3+4)/48

= 7/48

A, B, and C’s one-day work = 1/6

Now, C’s one-day work = 1/6 – 7/48

= (8-7)/48

= 1/48

C’s one-day work = 1/48

Therefore, C can complete the job in 48 days.

Summary:

## A can do a job in 16 days, and B can do the same job in 12 days. With the help of C, they can finish the job in 6 days only. Then, C alone can finish it in (a) 34 days, (b) 22 days, (c) 36 days, and (d) 48 days.

A can do a job in 16 days, and B can do the same job in 12 days. With the help of C, they can finish the job in 6 days only. Then, C alone can finish it in 48 days.

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