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A man does half as much work as his son in three fourth of the time. If they take 18 days to complete the work together, how many days will the son take to

Let the son complete work in x days . => work done by son in 1 day = 1/x

=> Father completes half work in 3x/4 days => He completes full work ( 1/2 work + 1/2work ) in 2 *3x/4 = 3x/2 days => Work done by father in 1 day = 1/ ( 3x/2 ) = 2/3x

Now

They take 18 days to complete = 1 work

=> 18 * ( work done by pa + work done by son in 1 day ) = 1

=> 18 * ( 1/x + 2/3x ) = 1

=> 18 ( 1 + 2 / 3 ) = x ( multiply by x on both sides )