TANCET 2022 Solved Papers

Concept:Work backwards from the final amounts, since reversing each game is the easiest way to find the starting money.Explanation:The sisters lose in alphabetical order: Suvarna, Tara, Uma and Vibha.After the 4th game, each sister has $\text{Rs. }32$.Vibha lost the 4th game.Before it, Suvarna, Tara and Uma had half of $\text{Rs. }32$, which is $\text{Rs. }16$ each.Vibha gave away $16 + 16 + 16 = 48$ rupees and still had $32$ rupees left at the end.So before the 4th game, Vibha had $32 + 48 = \text{Rs. }80$.Hence, after the 3rd game, the amounts were $(16, 16, 80, 16)$ in the order Suvarna, Tara, Uma, Vibha.Uma lost the 3rd game.Reverse it: Suvarna, Tara and Vibha had $\text{Rs. }8$ each, and Uma had $80 + 8 + 8 + 8 = \text{Rs. }104$.So after the 2nd game, the amounts were $(8, 8, 104, 8)$.Tara lost the 2nd game.Reverse it: Suvarna and Vibha had $\text{Rs. }4$ each, Uma had $\text{Rs. }52$, and Tara had $4 + 52 + 4 + 8 = \text{Rs. }68$.So after the 1st game, the amounts were $(4, 68, 52, 4)$.Suvarna lost the 1st game.Reverse it: Tara had $\text{Rs. }34$, Uma had $\text{Rs. }26$, and Vibha had $\text{Rs. }2$.Suvarna had $4 + 34 + 26 + 2 = \text{Rs. }66$.Answer:Suvarna started with $\text{Rs. }66$, which is option C.