A and B can do a piece of work in 12 days .B and C in 15 days ,C and A in 20 days how would A take separately to do the same work ?

Question

Solve it stepwise 

Answer 1

12(A + B) = 1 --->  A + B = 1/12

 

15(B+C) = 1  ---->  B + C = 1/15 

 

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

 

substituting the third equation into the second equation

 

B + (1/20 - A) = 1/15

 

B - A = 1/15 - 1/20

 

B - A = (20 -15)/300 = 5/300 = 1/60

 

B = A + 1/60

 

substituting this into the first equation:

 

A + A + 1/60 = 1/12

 

2A + 1/60 = 1/12

 

2A = 1/12 - 1/60

 

2A = 5/60 - 1/60 = 4/60 = 1/15

 

A = 1/30

 

C = 1/20 - 1/30 = (30 - 20)/600 = 10/600 = 1/60

 

B = A + 1/60 = 1/30 + 1/60 = 2/60 + 1/60 = 3/60 = 1/20

 

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A will take 30 days

 

B will take 20 days

 

C will take 60 days