Question

A and B can do a piece of work in 30 days and B and cc in 24 days . c and a in 40 days .How long will it take them to do the work together.
In what time can each finish it working alone​

Answer 1

Solution

Given :-

• A and B can do a piece of work in 30 days
• B and cc in 24 days
• c and a in 40 days .How

Find :-

• Time taken , if they work togather .

Explanation

According to question,

==> 1/A + 1/B = 1/30 ______(1)

And,

==> 1/B + 1/C = 1/24_______(2)

And,

==> 1/C + 1/A = 1/40_______(3)

Total working days , if they work togather

==> 2( 1/A + 1/B + 1/C) = 1/30 +1/24 + 1/40

==> 1/A + 1/B + 1/C = (4 + 5 + 3)/240

==> 1/A + 1/B + 1/C = 12/240

==> 1/A + 1/B + 1/C = 1/20

Since

• Total working days will be 20 days, if they work togather.

Now, Calculate working days of A's if they work alone

==> 1/A = 1/20- (1/B + 1/C)

==> 1/A = 1/20- (1/24)

==> 1/A = (6 - 5)/120

==> 1/A = 1/120

Similarly,

==> 1/B = 1/20 - (1/C + 1/A)

==>1/B = 1/20 - 1/40

==> 1/B = (2-1)/40

==> 1/B = 1/40

And,

==> 1/C = 1/20 - (1/A + 1/B)

==> 1/C = 1/20 - 1/30

==> 1/C = (3-2)/60

==> 1/C = 1/60

Hence

• A take working of days = 120 days
• B take working of days = 40 days
• C take working of days = 60 days

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