The sum of two numbers is 234560. One number is 10010 greater than the other. What is the greater number?

Let the two numbers be $x$ and $y$.
From the problem statement, the sum of the two numbers is 234560:

$$x + y = 234560 \quad (1)$$

One number is 10010 greater than the other. Let $x$ be the greater number:

$$x = y + 10010$$

Rearrange this equation to make it easier to solve with the first equation:

$$x - y = 10010 \quad (2)$$

Add equation (1) and equation (2):

$$(x + y) + (x - y) = 234560 + 10010$$ $$2x = 244570$$

Divide by 2 to find $x$:

$$x = \frac{244570}{2}$$ $$x = 122285$$

Substitute the value of $x$ into equation (1):

$$122285 + y = 234560$$ $$y = 234560 - 122285$$ $$y = 112275$$

The two numbers are 122285 and 112275. The greater number is 122285.
Comparing this with the given options:
(A) 112275
(B) 122285
(C) 132285
(D) 117280

The correct option is (B).

The greater number is $\boxed{\text{B) } \textbf{122285}}$.