# Time and Work | PRMO-2017 | Problem 3

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

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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