in Dash Cat 2 first set of balloon-awards in that the last question's solution it is unclear to me as to how the Ramit can get 145 only when sumit is earning max why can it not be the case that sumit is earning lower because we have capped the money earned by ramit which is 145 that too the combo is only via 55, 40, 45 when 45 is already taken by Amit???

please help

Hi, so the question states the maximum profit earned by Ramit is Rs.115 which means he scored a total of Rs. 145 only. Now this is because in the start of the set they mention the player has to pay Rs 10 for each throw. So basically Ramit spent Rs. 30 as everyone takes 3 throws. Total profit= Total amount after bursting 3 balloons - Amount paid for all the throws. We know total profit is 115 and amount paid by him for the throws is 30. Hence, he can only earn 145. since we are trying to maximise here we have to see the maximum numbers ramit can hit. 145 is made with the combination of 55,50 and 40. Now since sumit went before Ramit he would have hit the maximum Rs. balloons too otherwise ramit could have earned a higher profit. After Amits throw of 60,65 and 45, we are left with 80,75,70,55,50,40,35,25,20,15,10,5. Now that sumit goes he will hit the maximum Rs. balloons which is 80+75+70=225 and now since he spent 30 for the entry throw. His total profit will be 225-30= 195 and after that ramit goes and hits 55,50 and 40. Hope this helps!