Keith and Steve complete a work in 12days . => Keith and Steve do 1/12 work per day . => In half a day Keith and Steve together do 1/24 work.
Keith similarily does 1/20 work per day .
=> In half a day Keith does 1/40 work .
The condition -> ( Keith works half a day and steve works full day ) = the condition ->( Keith and steve work half a day + steve works further more 1/2 day without keith )
So work done in a day = ( 1/24 + 1/40 ) = 1/15
So total days taken = 1/ ( 1/15 ) = 15 days .