Three friends, R, S and T shared toffee from a bowl. R took 1/3rd of the toffees, but returned four to the bowl. S took 1/4th 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 17 toffees left, how many toffees were originally there in the bowl?
Options:
(A) 38
(B) 31
(C) 48
(D) 41
Official Answer Key:
C
Step-by-Step Solution & Explanation
Work backward from the final count. After T's turn, 17 remain (T already returned 2, so before that return the bowl held 15, which is exactly 'half the remainder T left behind' — meaning before T's turn the bowl held X where X/2 = 15 ⇒ X = 30). Before S's turn, S took 1/4 and returned 3, leaving 30; before that return, the bowl held 27, which is 3/4 of what was there before S's turn (S took away 1/4): Y×(3/4) = 27 ⇒ Y = 36. Before R's turn, R took 1/3 and returned 4, leaving 36; before that return, the bowl held 32, which is 2/3 of the original amount Z (R took 1/3 away): Z×(2/3) = 32 ⇒ Z = 48, matching option (C).
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