Question

If (146)_x + (313)_x-2 = (246)₈, then the value of base x is:
1. 5
2. 6
3. 7
4. 9

Answer 1

Correct Answer - Option 3 : 7

Concept:

To determine the decimal equivalent of a given number in base r, we use the following method:

Let the number given is (ABC)_r.

The decimal equivalent will be:

(ABC)₁₀ = (A × r²) + (B × r¹) + (C × r⁰)

Calculation:

(146)x + (313)x-2 = (246)8

Converting the equation into common base 10

x² + 4.x + 6 + 3.(x - 2)² + (x - 2) + 3.(x - 2)⁰ = 2 × 8² + 4 × 8 + 6 × 8⁰

x2 + 4.x + 6 + 3.(x² + 4 - 4x) + (x - 2) + 3 = 166

4x² - 7x + 19 - 166 = 0

4x2 - 7x - 147 = 0

On solving the quadratic equation we get,

x = 7 and  x = -21/4

As x cannot be a negative integer,

Therefore, x = 7