1. A can do a work in 12 days. When he had worked for 3 days, B joined him. If they complete the work in 3 more days, in how many days can B alone finish the work?
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By: anil on 05 May 2019 02.00 am
Let the rate of work done by A and B $$ frac{1}{A} and frac{1}{B} $$
$$frac{1}{A} = frac{1}{12}$$
Work done by A in 3 days = $$3 imes frac{1}{A} = frac{3}{12} = frac{1}{4}$$
In 3 more days A and B together completed the remaining $$ frac{3}{4}$$th of the work.
$$3 imes (frac{1}{A} + frac{1}{B}) = frac{3}{4}$$
$$ (frac{1}{A} + frac{1}{B}) = frac{1}{4}$$
$$ (frac{1}{12} + frac{1}{B}) = frac{1}{4}$$
$$ frac{1}{B}= frac{1}{4} - frac{1}{12}$$
$$ frac{1}{B}= frac{3-1}{12} = frac{2}{12} = frac{1}{6} $$
B alone can complete the work in 6 days.
Hence Option A is the correct answer.
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$$frac{1}{A} = frac{1}{12}$$
Work done by A in 3 days = $$3 imes frac{1}{A} = frac{3}{12} = frac{1}{4}$$
In 3 more days A and B together completed the remaining $$ frac{3}{4}$$th of the work.
$$3 imes (frac{1}{A} + frac{1}{B}) = frac{3}{4}$$
$$ (frac{1}{A} + frac{1}{B}) = frac{1}{4}$$
$$ (frac{1}{12} + frac{1}{B}) = frac{1}{4}$$
$$ frac{1}{B}= frac{1}{4} - frac{1}{12}$$
$$ frac{1}{B}= frac{3-1}{12} = frac{2}{12} = frac{1}{6} $$
B alone can complete the work in 6 days.
Hence Option A is the correct answer.