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: 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
