## Friday, 21 October 2011

### Arithmetic -4 (CSAT-2011)

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
(B) 31
(C) 48
(D) 41
Solution 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