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: 1 year ago | Updated: 1 year ago
Updated: 1 year ago

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 = (118) part of work

Similarly, (B+C) take 1 day to complete =124 part of work

And (A+C) take 1 day to complete = 136 part of work

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

=118+124+136=4+3+272=972 Part of work

2(A+B+C) take 1 day to complete =18 Part of work

(A+B+C) take 1 day to complete =18×2=116 Part of work

116 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 =1×161=16 days

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

Or, 116-136=5144 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, 116-118=5144 

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, 116-118=1144 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 

1 year ago

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