B's one day work = [latex]\frac {1}{18}[/latex]

(A + B)'s one day work = [latex]\frac {1}{12} + \frac {1}{18} = \frac {(18 + 12)}{(12 \times 18)} = \frac {30}{216} = \frac {1}{7.2}[/latex]

Together, A & B will finish the work in 7.2 days.

B's one day work = [latex]\frac {1}{5}[/latex]

C's one day work = [latex]\frac {1}{10}[/latex]

(A+ B+ C)'s one day work = [latex]\frac {1}{3} + \frac {1}{5} = \frac {1}{10} = \frac {1}{1.5} [/latex]

Hence, A ,B & C together will take 1.5 days to complete the work.

As painters P1 & P2 paint the bungalows in 3 days, then work done by both painters = [latex]\frac {1}{3}[/latex]

As P1 paint it alone in 12 days, then work done by painter P1 = [latex]\frac {1}{12}[/latex]

Work done by painter P2 = [latex]\frac {1}{3} - \frac {1}{12} = \frac {4 - 1}{12} = \frac {3}{12} = \frac {1}{4} [/latex]

Therefore, same work will be completed by painter P2 in 4 days.

We can write, (A + B + C)'s 1 day work = [latex]\frac {1}{4}[/latex]

Similarly, (A+B) 's 1 day work = 1/6 days & (B+C)'s 1 day work = [latex]\frac {1}{10}[/latex]

Since the work is divided in combination and we are asked to find out the combined work of (A + C), so we can find out,

(A + C)'s 1 day work = [2 (A+B+C)'s 1 day work] – [(A+ B) 's 1 day work + (B+C)'s 1 day work]

[latex][2 \times \frac {1}{4}] - [(\frac {1}{6}) + (\frac {1}{10})][/latex]

[latex][ \frac {1}{2}] - \frac {16}{60} = \frac {1}{2} - \frac {4}{15} = \frac {7}{30}[/latex]

Hence, A & C together can complete the work in [latex]\frac {30}{7} days = 4 \frac {2}{7} days[/latex]

Assume that Pooja completes the job in 'x' days.

So, Aarti will take '2x' days to complete the same job.

As Pooja takes 90 days less than Aarti, we get

x = 2x – 90

By solving this equation, we get x = 90 .

Thus, 2x = 2 x 90 = 180

Part of job done by Pooja in 1 day = [latex]\frac {1}{90}[/latex]

Part of job done by Aarti in 1 day = [latex]\frac {1}{180}[/latex]

(Part of job done together in 1 day) = (Part of job done by Pooja in 1 day) + (Part of job done by Aarti in 1 day)

= [latex]\frac {1}{90} + \frac {1}{180}[/latex]

= [latex]\frac {3}{180}[/latex]

=[latex]\frac {1}{60}[/latex]

([latex]{(\frac {1}{60})}^{th}[/latex]) part of whole job will be completed by Pooja and Aarti together in one day.

Therefore, the whole job will be completed in 60 days together.

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