Q.X and y are natural numbers such tgat they satisfy the equation x + y = 3xy. Find the maximum possible integral power of 6 in (xy)!. In solution it has been mentioned that 11 and 1 will be the last trial and error pair and has asked us to guess the reasone why. I could not figure it out could any one please explain it to me.

A labourer is paid Rs. 8 per hour for an 8 hour day and 1.5 times that rate for each hour in excess of 8 hours in a single day. If the labourer received Rs. 80 for a single day's work, how long did he work on that day? (a) 6 hrs 40 min (b) 9 hrs 20 min (c) 9 hrs 30 min (d) 9 hrs 40 min (e) 10 hrs

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b) 9 hrs 20min . 8*8 =64 , and the 8*1.5= 12 . so total 76 rs . if 12 rs/hour is to be paid so for left 4 rs which is 12/3 labourer has to work for 1/3 of an hour which is 20 min . simple