Three friends R,S and T shared toffees from a bowl. R took 1/3rd of the
toffees, but returned 4 to the bowl. S took 1/4th of what was left but returned
3 toffees to the bowl. T took 2/3rd of what was left but returned 7 toffees to
the bowl. If the bowl had 17 toffees left, how many toffees were originally
there in the bowl?

(A) 38

Solution follows here:

(A) 38

(B) 31

(C) 48

(D) 41Solution follows here:

Solution:

Let x be the number of toffees originally
there in the bowl.

R took 1/3rd of the toffees, but returned
4 to the bowl:

R took x/3 and returned 4

=> Toffees left out in the bowl =
(1-1/3)x + 4 = (2x/3) + 4 = (2x+12)/3

S took 1/4th of what was left but returned
3 toffees to the bowl:

=> Toffees left out in the bowl =
(1-1/4) (2x+12)/3 + 3 = (3/4) (2x+12)/3 + 3

= (x+6)/2 + 3 = (x+6+6)/2 = (x+12)/2

T took 2/3rd of what was left but returned
7 toffees to the bowl

=> Toffees left out in the bowl = (1-2/3)
(x+12)/2 + 7 = (1/3) (x+12)/2 + 7

= (x+12)/6 + 7

Given that the bowl had 17 toffees left
=> (x+12)/6 + 7 = 17

=> (x+12)/6 = 10 => x+12 = 60 =>
x = 48

**Answer (C)**
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