Let the temp at the intersection of the three rods is T .Since at steady state rate of heat transfer is same, KA\\dfrac{(90-T)}{x} + KA\\dfrac{(90-T)}{x} = KA\\dfrac{(T-10)}{x} \\Rightarrow 2(90-T)= T-10 \\Rightarrow T={\\dfrac{190}{3}}^0C