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  • 9. A and B can do a piece of work in 30 days: B and C in 24 days; C and A in 40 days. How long willit take them to do the work togetherIn what time can each finish it, working alone?​

9. A and B can do a piece of work in 30 days: B and C in 24 days; C and A in 40 days. How long willit take them to do the work togetherIn what time can each finish it, working alone?​

Answers (1)

A and B can do a piece of work in = 40 days
B and C can do a piece of work in = 30 days
C and A can do a piece of work in = 24 days
(A+B)’s 1 day work = 1/40
(B+C)’s 1 day work = 1/30
(C+A)’s 1 day work = 1/24
So, [(A+B)+(B+C)+(C+A)]’s 1 day work =  1/40 + 1/30 + 1/24= (3 + 4 + 5)/120= 12/120 = 1/10

i.e. (A + B + B + C + C + A)’s 1 day work = 1/10

i.e. 2(A + B + C)’s 1 day work = 1/10

∴ (A + B + C)’s 1 day work = 1/20

∴ (A + B + C) can do the work in = 20 days

A’s 1 day work = 1/20 – 1/30= (3 – 2)/60 = 1/60
∴ A can do the work in 60 days

B’s 1 day work = 1/20 – 1/24= (6 – 5)/120 = 1/120
∴  B can do the work in 120 days

Now, C’s 1 day work = 1/20 – 1/40= (2 – 1)/40 = 1/40
∴ C can do the work in 40 days 

Posted by

shubham.krishnan

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