A and B can do a work in 8 days, B and C in 12 days, and A and C in 16 days.

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asked May 15 in Class VIII Maths by priya12 (-11,279 points)

A and B can do a work in 8 days, B and C in 12 days, and A and C in 16 days. In what time could they do it all working together ?

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1 Answer

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answered May 15 by navnit40 (-2,750 points)

A and B can do a work in = 8 days
B and C can do a work in = 12 days
A and C can do a work in = 16 days
(A+B)’s 1 day work = 
(B+C)’s 1 day work = 

(A + C)’s 1 day work = 1/16

∴ [(A + B) + (B + C) + (A + C)]’s 1 day work

= 1/8 + 1/12 + 1/16

i.e. [A + B + B + C + A + C]’s 1 day work

= 1/8 + 1/12 + 1/16

= (6 + 4 + 3)/48 = 13/48

i.e. 2(A + B + C)’s 1 day work = 13/48

i.e. (A + B + C)’s 1 day work = 13/48 × ½ = 13/96

∴  (A + B + C) can do the work in = 96/13 days

= 7. 5/13 days.

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