Correct Option: C

By observation of summation, it can be seen that numbers are not in decimal. Let they have base n. Then converting all number in decimal
(137)_n = [ 1 × n² + 3n + 7n⁰ ]₁₀
(276)_n = [ 2n² + 7n + 6n⁰ ]₁₀
(435)_n = [ 4n² + 3n + 5n⁰ ]₁₀
(731)_n = [ 7n² + 3n + 1n⁰ ]₁₀
(672)_n = [ 6n² + 7n + 2n⁰ ]₁₀
∴ (137)_n + (276)_n = (435)_n
⇒ n² + 3n + 7 + 2n² + 7n + 6n = 4n² + 3n + 5
⇒ n² – 7n – 8 = 0 ⇒ n = – 1, 8
Possible base n = 8 (+ ve)
(435)_n = (435)₈ = [ 4 × 8² + 3 × 8 + 5 ]₁₀ = (285)₁₀
(731)_n = (731)₈ = [ 7 × 8² + 3 × 8 + 1 ]₁₀ = (473)₁₀
(672)_n = (672)₈ = [ 6 × 8² + 7 × 8 + 2 ]₁₀ = (442)₁₀
So , (731)₈ + (672)₈ = (473)₁₀ + (442)₁₀ = (915)₁₀
(915)₁₀ = (1623)₈