Categories

# Time & Work Problem | PRMO-2017 | Problem 3

Try this beautiful problem from Pre-Regional Mathematics Olympiad, PRMO, 2017 based on Time & Work. You may use sequential hints to solve the problem.

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

Answer:$16$

PRMO-2017, Problem 3

Pre College Mathematics

## Try with Hints

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 ……….

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 $\frac{1}{12} +\frac{1}{36}$=$\frac{1}{9}$

Now according to question,
Let more number of days should team B works to complete the job be x days

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

$\Rightarrow x=16$