Correct Option: C

Let the two numbers be P and Q.
According to given question,
Sum of two numbers = 24
∴ P + Q = 24 ...................... (1)
Product of two numbers = 143
and, PQ = 143 .......................... (2)
As we know the formula,
∴ P ² + Q² = (P + Q)² – 2PQ
Put the value from the equation (1) and (2), We will get
∴ P ² + Q² = (24)² – 2 × 143
∴ P ² + Q² = 576 – 286 = 290