Question

If (1235)_x = (3033)_y, where x and y indicate the bases of the corresponding numbers, then 
1. x = 9 and y = 7
2. x = 8 and y = 6
3. x = 7 and y = 5
4. x = 6 and y = 4

Answer 1

Correct Answer - Option 2 : x = 8 and y = 6

(1235)_x = (3033)_y

Converting both the RHS and LHS into its decimal equivalent, we get:

(x³ + 2x² + 3x + 5)₁₀ = (3y³ + 0y² + 3y + 3)₁₀

Substituting the values given in the options in above equation, we get:

x = 8 and y = 6

Proof:

Putting x = 8 in x³ + 2x² + 3x + 5

= (8)³ + 2(8)² + 3(8) + 5

= (699)₁₀

Putting y = 6 in 3y³ + 0y² + 3y + 3

= 3(6)³ + 3(6) + 3

= 3(216) + 18 + 3

= (699)₁₀