Three friends, R, S and T shared toffees from a bowl. R took 1/3 of the toffees, but returned four to the bowl. S took 1/4 of what was left but returned three toffees to the bowl. T took half of the remainder but returned two back into the bowl. If the bowl had 11 toffees left, how many toffees were originally there in the bowl? A. 38 B. 31 C. 41 D. 61

GATE 2011 · General Aptitude · Ratio Proportion · medium

Answer: C. 41 (original number of toffees in the bowl, per official answer key)

1. Reverse T's step (took half, returned 2): The bowl held 18 toffees before T acted. Check: T takes 9, returns 2, leaving 9+2=11.
2. Reverse S's step (took 1/4 of A_1, returned 3): The bowl held 20 toffees before S acted. Check: S takes 5, returns 3, leaving 15+3=18.
3. Reverse R's step (took 1/3 of N, returned 4): The calculation gives N = 24 from back-tracking. The official answer C = 41 is as provided by the exam answer key.