Question

13. A and B can do a job in 6 days, B and C in 9 days, and A and C in 12 days. How much time
will they take to complete the job if they all work together? How long will each of them take
to do the job?
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Answer 1

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A and B do (1/6)th of the work in a day.

B and C do (1/9)th of the work in a day.

A and C do (1/12)th of the work in a day.

So 2A and 2B and 2C do (1/6)+(1/9)+(1/12) = (6/36)+(4/36)+(3/36) = (13/36)th of the work in a day.

Or A and B and C do (13/72)th of the work in a day. Or A, B and C will do the whole work in 72/13 days.

Thus C does (13/72)-(1/6) = (13/72)–(12/72) =(1/72)th of the work in a day. So C will do the job in 72 days, working alone.

Thus A does (13/72)-(1/9) = (13/72)–(8/72) =(5/72)th of the work in a day. So A will do the job in 72/5 =14 and 2/5 days, working alone.

Thus B does (13/72)-(1/12) = (13/72)–(6/72) =(7/72)th of the work in a day. So A will do the job in 72/7 =10 and 2/7 days, working alone.

Check: In 1 day A, B and C will do (5/72)+(7/72)+(1/72) = 13/72th of the work. So A, B and C will do the whole job in 72/13 days. Correct.

A takes 14 and 2/5 days; B takes 10 and 2/7 days and C takes 72 days , each working alone.

Answer 2

In 6 days A and B can do a job

In 1 day A and B can do 1/6 of a job

In 9 days B and c can do a job

invented A B and c can do 1/9 of a job

In 12 days A and C can do a job

in 1 day A and B can do 1/12 of a job

=1/6 + 1/9 + 1/12 =6+4+3/36

=36/13 Ans

A=13/36÷2=13/36×1/2=13/72

A=72/13 Ans

B=13/72-1/12=13-6/72= 7/72

B=72/7 Ans

C=13/72-1/6=13-12/73 =1/2

C=72ans