Try this beautiful problem from PRMO, 2017 from Arithmetic based on Time & Work.

## Time & Work Problem | PRMO | Problem 3

A contractor has two teams of workers: team A and team B. Team A can complete a job in 12 days and team B can do the same job in 36 days. Team A starts working on the job and team B joins A after four days. Team A withdraws after two more days. For how many more days should team B work to complete the job?

- \(24\)
- \(16\)
- \(22\)
- \(18\)

**Key Concepts**

Arithmetic

Unitary process

Work done

## Check the Answer

But try the problem first…

Answer:\(16\)

PRMO-2017, Problem 3

Pre College Mathematics

## Try with Hints

First hint

At first we have to find out A’s 1 days work and B’s 1 days work.next find out A and B both together 1 day’s work .

Can you now finish the problem ……….

Second Step

Team A completes job in 12 days and Team B completes job in 36 days

1 day work of team A =\(\frac{1}{12}\)

1 day work of team B=\(\frac{1}{36}\)

1 day work of team A and team B (when they both work together \(\frac{1}{12} +\frac{1}{36}\)=\(\frac{1}{9}\)

Final Step

Now according to question,

Let more number of days should team B works to complete the job be x days

\(4 \times \frac{1}{12} +2 \times \frac{1}{9} + x \times \frac{1}{36}=1\)

\(\Rightarrow x=16\)

## Other useful links

- https://www.cheenta.com/probability-in-divisibility-amc-10a-2003-problem-15/
- https://www.youtube.com/watch?v=pLAMlNUOdTs

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