Try this beautiful problem from PRMO, 2017 based on Time and 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 team A after four days. The team A withdraws after two more days. For how many more days should team B work to complete the job ?
Arithmetic
multiplication
unitary method
But try the problem first...
Answer:$16$
PRMO-2017, Problem 3
Pre College Mathematics
First hint
In the problem,we notice that first 4 days only A did the work.so we have to find out A's first 4 days work done.next 2 days (A+B) did the work together,so we have to find out (A+B)'s 2 days work.
so we may take the total work =1
A's 1 day's work= \(\frac{1}{12}\) and B's 1 day's work=\(\frac{1}{36}\)
Can you now finish the problem ..........
Second Hint
Now B did complete the remaining work.so you have to find out the remaining work and find out how many more days taken....
so to find the remaining work subtract (A's 4 day;s work + (A+B)'S 2 days work)) from the total work
Can you finish the problem........
Final Step
Let the total work be 1
A can complete the total work in 12 days,so A'S 1 day's work=\(\frac{1}{12}\)
B can complete the total work in 36 days, so B's 1 day's work=\(\frac{1}{36}\)
First 4 days A's workdone=\(\frac{4}{12}=\frac{1}{3}\)
After 4 days B joined and do the work with A 2 days
So \((A+B)\)'s 2 day's workdone=\(2 \times( \frac{1}{12}+\frac{1}{36})\)=\(\frac{2}{9}\)
Remaining workdone=\((1-\frac{1}{3}-\frac{2}{9}\))=\(\frac{4}{9}\)
B will take the time to complete the Remaining work=\(36 \times \frac{4}{9}\)=16
Hence more time taken=16
AMC - AIME Boot Camp... for brilliant students.
Use our exclusive one-on-one plus group class system to prepare for Math Olympiad
Try this beautiful problem from PRMO, 2017 based on Time and 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 team A after four days. The team A withdraws after two more days. For how many more days should team B work to complete the job ?
Arithmetic
multiplication
unitary method
But try the problem first...
Answer:$16$
PRMO-2017, Problem 3
Pre College Mathematics
First hint
In the problem,we notice that first 4 days only A did the work.so we have to find out A's first 4 days work done.next 2 days (A+B) did the work together,so we have to find out (A+B)'s 2 days work.
so we may take the total work =1
A's 1 day's work= \(\frac{1}{12}\) and B's 1 day's work=\(\frac{1}{36}\)
Can you now finish the problem ..........
Second Hint
Now B did complete the remaining work.so you have to find out the remaining work and find out how many more days taken....
so to find the remaining work subtract (A's 4 day;s work + (A+B)'S 2 days work)) from the total work
Can you finish the problem........
Final Step
Let the total work be 1
A can complete the total work in 12 days,so A'S 1 day's work=\(\frac{1}{12}\)
B can complete the total work in 36 days, so B's 1 day's work=\(\frac{1}{36}\)
First 4 days A's workdone=\(\frac{4}{12}=\frac{1}{3}\)
After 4 days B joined and do the work with A 2 days
So \((A+B)\)'s 2 day's workdone=\(2 \times( \frac{1}{12}+\frac{1}{36})\)=\(\frac{2}{9}\)
Remaining workdone=\((1-\frac{1}{3}-\frac{2}{9}\))=\(\frac{4}{9}\)
B will take the time to complete the Remaining work=\(36 \times \frac{4}{9}\)=16
Hence more time taken=16
AMC - AIME Boot Camp... for brilliant students.
Use our exclusive one-on-one plus group class system to prepare for Math Olympiad
