Try this beautiful problem from PRMO, 2017 from Arithmetic based on Time & Work.
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?
Arithmetic
Unitary process
Work done
But try the problem first...
Answer:\(16\)
PRMO-2017, Problem 3
Pre College Mathematics
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
\(4 \times \frac{1}{12} +2 \times \frac{1}{9} + x \times \frac{1}{36}=1\)
\(\Rightarrow x=16\)
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Use our exclusive one-on-one plus group class system to prepare for Math Olympiad
Try this beautiful problem from PRMO, 2017 from Arithmetic based on Time & Work.
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?
Arithmetic
Unitary process
Work done
But try the problem first...
Answer:\(16\)
PRMO-2017, Problem 3
Pre College Mathematics
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
\(4 \times \frac{1}{12} +2 \times \frac{1}{9} + x \times \frac{1}{36}=1\)
\(\Rightarrow x=16\)
AMC - AIME Boot Camp... for brilliant students.
Use our exclusive one-on-one plus group class system to prepare for Math Olympiad
