Correct Answer: 36

Solution : Given: (a + b + c) = 12 and (ab + bc + ca) = 47.
On squaring both sides of the equation, (a + b + c) = 12, we get,
(a + b + c) ² = 12 ²
⇒ a ² + b ² + c ² + 2(ab + bc + ca) = 144
⇒ a ² + b ² + c ² + 2(47) = 144
⇒ a ² + b ² + c ² = 144 – 94
⇒ a ² + b ² + c ² = 50
The value of (a ³ + b ³ + c ³ – 3abc) is,
a ³ + b ³ + c ³ – 3abc = (a + b + c)(a ² + b ² + c ² – (ab + bc + ca))
⇒ a ³ + b ³ + c ³ – 3abc = 12(50 – 47)
⇒ a ³ + b ³ + c ³ – 3abc = 12 × 3
$\therefore$ a ³ + b ³ + c ³ – 3abc = 36
Hence, the correct answer is 36.