Question

A and B can complete a work in 6 days. B and C can complete the same work in 8 days. C and A can complete in 12 days. How many days will take for A, B and C combined together to complete the same amount of work ?​

Answer 1

QUESTION:-

A and B can complete a work in 6 days. B and C can complete the same work in 8 days. C and A can complete in 12 days. How many days will take for A, B and C combined together to complete the same amount of work ?

SOLUTION:-

From the given information, we can have 

(A + B)'s 1 day work  =  1/6

(B + C)'s 1 day work  =  1/8

(A + C)'s 1 day work  =  1/12

(A + B + B + C + A + C)'s 1 day work  =  1/6 + 1/8 + 1/12

(2A + 2B + 2C)'s 1 day work  =  1/6 + 1/8 + 1/12

2 ⋅ (A + B + C)'s 1 day work  =  1/6 + 1/8 + 1/12

L.C.M of (6, 8, 12)  =  24. 

Then, we have

2 ⋅ (A + B + C)'s 1 day work  =  4/24 + 3/24 + 2/24

2 ⋅ (A + B + C)'s 1 day work  =  9 / 24

2 ⋅ (A + B + C)'s 1 day work  =  3 / 8

(A + B + C)'s 1 day work  =  3 / (2 ⋅ 8)

(A + B + C)'s 1 day work  =  3 / 16

Time taken by A, B and C together to complete the work is

=  16 / 3

=  5 ⅓ days

Answer 2

Answer:

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