Doubt in Macroeconomics ( ISI 2015)

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Doubt in Macroeconomics ( ISI 2015)

Econenthusiast
Could somebody please tell me how the household optimisation problem is solved for the above question .I read the answer which was provided by Amit sir, but still cant understand that bit. I'm getting stuck there, somebody please help me out. The link to the question and the answer is provided below:

http://www.econschool.in/stuff-of-interest/isi-exams/isi-2015-q06