1. A and B can complete a piece of work in 8 days, B and C can do it in 12 days, C and A can do it in 8 days. A, B and C together can complete it in
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By: anil on 05 May 2019 02.00 am
Let the rate of work done by A, B and C be $$ frac{1}{A} , frac{1}{B} and frac{1}{C}$$
$$(frac{1}{A} + frac{1}{B}) = frac{1}{8}$$ ------------------- 1
$$(frac{1}{B} + frac{1}{C}) = frac{1}{12}$$ ------------------- 2
$$(frac{1}{A} + frac{1}{C}) = frac{1}{8}$$ ------------------- 3
Adding 1 , 2 and 3
$$2 imes (frac{1}{A} + frac{1}{B} + frac{1}{C}) = frac{1}{8} + frac{1}{12} + frac{1}{8} = = frac{1}{4} + frac{1}{12} = frac{1}{3} $$
$$(frac{1}{A} + frac{1}{B} + frac{1}{C}) = frac{1}{6}$$
It takes 6 days for all to complete the work.
Hence Option C is the correct answer.
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$$(frac{1}{A} + frac{1}{B}) = frac{1}{8}$$ ------------------- 1
$$(frac{1}{B} + frac{1}{C}) = frac{1}{12}$$ ------------------- 2
$$(frac{1}{A} + frac{1}{C}) = frac{1}{8}$$ ------------------- 3
Adding 1 , 2 and 3
$$2 imes (frac{1}{A} + frac{1}{B} + frac{1}{C}) = frac{1}{8} + frac{1}{12} + frac{1}{8} = = frac{1}{4} + frac{1}{12} = frac{1}{3} $$
$$(frac{1}{A} + frac{1}{B} + frac{1}{C}) = frac{1}{6}$$
It takes 6 days for all to complete the work.
Hence Option C is the correct answer.