Three boys shared some oranges. The first received (frac{1}{3}) of the oranges, the second received (frac{2}{3}) of the remainder. If the third boy received the remaining 12 oranges, how many oranges did they share?

A.
60 
B.
54 
C.
48 
D.
42
Correct Answer: Option B
Explanation
let x represent the total number of oranges shared, let the three boys be A, B and C respectively. A received (frac{1}{3}) of x, Remainder = (frac{2}{3}) of x . B received (frac{2}{3}) of remainder (i.e.) (frac{2}{3}) of x
∴ C received (frac{2}{3}) of remainder ((frac{2}{3}) of x) = 12
(frac{1}{3}) x (frac{2x}{3}) = 12
2x = 108
x = 54