1. A and B together can do a work in 10 days. B and C together can do the same work in 6 days. A and C together can do the work in 12 days. Then A, B and C together can do the work in
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By: anil on 05 May 2019 02.01 am
A and B togeather complete 1/10 th of work in a day.
$$(frac{1}{A} + frac{1}{B}) = frac{1}{10}$$ --------------- 1
B and C togeather complete 1/6 th of work in a day.
$$(frac{1}{B} + frac{1}{C}) = frac{1}{6}$$ ----------------- 2
A and C togeather complete 1/12 th of work in a day.
$$(frac{1}{A} + frac{1}{C}) = frac{1}{12}$$ --------------- 3
Adding 1 ,2 and 3
$$2 imes(frac{1}{A} + frac{1}{B} + frac{1}{C}) = frac{1}{10} + frac{1}{6} + frac{1}{12}$$
Taking LCM we get
$$frac{1}{10} + frac{1}{6} + frac{1}{12} = frac{6+10+5}{60} = frac{21}{60} $$
$$(frac{1}{A} + frac{1}{B} + frac{1}{C})= frac{21}{120}$$
A B and C complete 21/120 th of the work in a day.
In 5 days they would complete 105/120th of the work.
At the end of 6th day they would have completed 126/120 th of work (Which is greater than 1)
Hence they finish the entire work before the end of 6th day.
Out of the given options Option C suits the best.
Hence Option C is the correct answer.
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$$(frac{1}{A} + frac{1}{B}) = frac{1}{10}$$ --------------- 1
B and C togeather complete 1/6 th of work in a day.
$$(frac{1}{B} + frac{1}{C}) = frac{1}{6}$$ ----------------- 2
A and C togeather complete 1/12 th of work in a day.
$$(frac{1}{A} + frac{1}{C}) = frac{1}{12}$$ --------------- 3
Adding 1 ,2 and 3
$$2 imes(frac{1}{A} + frac{1}{B} + frac{1}{C}) = frac{1}{10} + frac{1}{6} + frac{1}{12}$$
Taking LCM we get
$$frac{1}{10} + frac{1}{6} + frac{1}{12} = frac{6+10+5}{60} = frac{21}{60} $$
$$(frac{1}{A} + frac{1}{B} + frac{1}{C})= frac{21}{120}$$
A B and C complete 21/120 th of the work in a day.
In 5 days they would complete 105/120th of the work.
At the end of 6th day they would have completed 126/120 th of work (Which is greater than 1)
Hence they finish the entire work before the end of 6th day.
Out of the given options Option C suits the best.
Hence Option C is the correct answer.