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 is B

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