A ও B একটি কাজ 18 দিনে, B ও C 24 দিনে এবং A ও C 36 দিনে করতে পারে। ঐ কাজটি তারা একত্রে আলাদাভাবে কয়দিনে করবে?

(A+B) take 18 days to complete= 1 work

(A + B) take 1 day to complete = ($\frac{1}{18}$) part of work

Similarly, (B+C) take 1 day to complete =$\left(\frac{1}{24}\right)$ part of work

And (A+C) take 1 day to complete = $\left(\frac{1}{36}\right)$ part of work

On adding, [(A+B)+(B+C)+(A+C)] take 1 day to complete

=$\left(\frac{1}{18}+\frac{1}{24}+\frac{1}{36}\right)=\left(\frac{4+3+2}{72}\right)=\left(\frac{9}{72}\right)$ Part of work

2(A+B+C) take 1 day to complete =$\left(\frac{1}{8}\right)$ Part of work

$\Rightarrow (A+B+C) take 1 day to complete =\left(\frac{1}{8\times 2}\right)=\left(\frac{1}{16}\right) Part of work$

$\frac{1}{16}$ Part of work is done by (A+B+C) in 1 day

$\therefore$ 1 or complete part of work is done by (A+B+C) in =$\frac{1\times 16}{1}=16$ days

Only A can do the work (A+B+C)-(B+C)

Or, $\frac{1}{16}-\frac{1}{36}=\frac{5}{144}$ part in 1 day.

So, A can complete the whole work in 48 days

Now, Only B can do the work (A+B+C)-(A+C)

$or, \frac{1}{16}-\frac{1}{18}=\frac{5}{144}$ 

So, B can complete the whole work in 28.8 or 29 days.

And only C can do the work (A+B+C)-(A+B)

$or, \frac{1}{16}-\frac{1}{18}=\frac{1}{144}$ part in I day. 

So, C can complete the whole work in 144 days

ans. Working together A, B and C finish the work in 16 days and separately A, B and C finish the we in 48 days, 29 days & 144 days respectively