Mathematics

A and B can do a piece of work in 18 days; B and C can do it in 24 days; A and C can do it in 36 days. In how many days will A, B and C finish it, working together and separately?

Created: 2 months ago | Updated: 2 months ago

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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 = $(\frac{1}{24})$ part of work

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

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

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

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

$\Rightarrow (A + B + C) t a k e 1 d a y t o c o m p l e t e = (\frac{1}{8 \times 2}) = (\frac{1}{16}) P a r t o f w o r k$

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

$∴$ 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)

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

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)

$o r, \frac{1}{16} - \frac{1}{18} = \frac{1}{144}$ 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

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Mathematics

A and B can do a piece of work in 18 days; B and C can do it in 24 days; A and C can do it in 36 days. In how many days will A, B and C finish it, working together and separately?

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