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AMC-8 Math Olympiad USA Math Olympiad

Time and Work | PRMO-2017 | Problem 3

Try this beautiful problem from PRMO, 2017 based on Time and work. You may use sequential hints to solve the problem.

Try this beautiful problem from PRMO, 2017 based on Time and work.

Time and work | 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 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 ?

  • $20$
  • $16$
  • $13$

Key Concepts


Arithmetic

multiplication

unitary method

Check the Answer


Answer:$16$

PRMO-2017, Problem 3

Pre College Mathematics

Try with Hints


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 ……….

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……..

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

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