we knw the rate of heat flow is given by I = KA(T2-T1)/L
here L/KA can be considered as resistance of the rods.... we'll denote it by R
so now when temperature is maintained across A and C, we have an equivalent resistance of value R, across A and C....
thrfore 30X= (T2-T1)/R
now when it is maintained between A and D, we have an equivalent resistance of 3R/4
thrfore KX =4(T2-T1)/3R
now u can easily calculate the value of K and find the value of the required expression.......