GATE ECE 2021 | Question: 11

Question

​​​​​​​If $(1235)_{x}\:=\:(3033)_{y}$, where $x$ and $y$ indicate the bases of the corresponding numbers, then

• A. $x\:=\:7$ and $y\:=\:5$
• B. $x\:=\:8$ and $y\:=\:6$
• C. $x\:=\:6$ and $y\:=\:4$
• D. $x\:=\:9$ and $y\:=\:7$

Answer 1

Given equation is $(1235)_x = (3033)_y$

Convert both size to their decimal number system equivalent:

$x^3 + 2x^2 + 3x + 5 = 3y^3 + 3y + 3$

Now, substitute values from options in this equation.

Option B matches.