According to the definite conditions of the questions, the arrangement is- 
It is given that Varun does not take leave on Tuesday so Varun can take leave on Thursday or Saturday or Sunday. According to the question, the one who likes purple takes leave on the day just before the day on which Varun takes leave and three people takes leave between the days on which the one who likes yellow and the one who likes brown takes. The friend who likes green takes leave just before the day on which the one who likes red takes leave and the one who likes yellow takes leave after the day on which the one who likes red take. So, three conditions are applied on all the possible arrangements of Varun . in the first arrangement, when Varun takes leave on Saturday. So Amitabh likes purple. According to the condition, two friends take leave between the days on which the one who likes black & the one who likes white take leave that means two people takes leave between the days on which Varun and Hrithik takes leave . So, Hrithik takes leave on Monday but it is given that Rajesh takes leave on Monday. So this arrangement is not possible In the second arrangement, when Varun takes leave on Sunday so Hrithik takes leave on Wednesday but it is given that Amitabh takes leave on Wednesday. So this arrangement is also not possible. In the third arrangement, Varun takes leave on Thursday so Hrithik takes leave on Sunday. Sharukh likes purple . According to the given condition, Rajesh likes green , Salman likes red , Karthik likes brown colour and it is given that one who likes yellow takes leave after the day on which the one who likes red takes leave. So it can be any day after Tuesday. Only one friend remains so Amitabh likes yellow. 
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