Okay here is my explaination . Youngs modulus of a wire is given by Y= F/A*l/L where L is the change in lenght of the spring.So if we consider the spring to be cut into 2 halves one having a spring constant k₁ & other having spring constant k then k_eq= k₁*k/k₁+k. Substituting value of k₁ which is YA/L*K/YA/L+K = YAK/YA+KI. hence substituting this values iget my final answer.