GATE CS 2010 Q61 — General Aptitude

The given addition $137 + 276 = 435$ is performed in a non-decimal number system with base $r$.

To find the base $r$, we convert the numbers into their decimal equivalents:

Simplifying both sides:

Since the base $r$ must be a positive integer, we have $r = 8$ (octal system).

Now, we perform the addition $731_8 + 672_8$ in base 8:

• Units place: $1 + 2 = 3$ (no carry)
• Eights place: $3 + 7 = 10 = 1 \times 8 + 2 \implies 2$ with a carry of $1$
• Sixty-fours place: $7 + 6 + 1 \text{ (carry)} = 14 = 1 \times 8 + 6 \implies 6$ with a carry of $1$
• Next place: $1$ (from carry)

Putting it all together:

Thus, the correct option is C.