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?

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

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