Find the dissimilar number pair from the given options:

Let's analyze the simplified ratio of each given pair:
* Option A: $\frac{10}{15}=\frac{2}{3}⟹2:3$
* Option B: $\frac{15}{60}=\frac{1}{4}⟹1:4$
* Option C: $\frac{9}{12}=\frac{3}{4}⟹3:4$
* Option D: $\frac{5}{20}=\frac{1}{4}⟹1:4$

Alternatively, let's look at divisibility/multiples:

* In $(15,60)$, $60=15\times 4$ (The second number is exactly 4 times the first).
* In $(5,20)$, $20=5\times 4$ (The second number is exactly 4 times the first).
* In $(9,12)$, the ratio is $3:4$.
* In $(10,15)$, the ratio is $2:3$.

Looking at standard classification setups for this question layout, the pairing follows the definition where the second number is a direct integral multiple of the first or based on standard ratios. In the pairs $(15,60)$, $(9,12)$, and $(5,20)$, the ratio of the second number to the first reduces to factors matching a common system, or the pair $(10,15)$ is the only one where both are not part of an increasing multiple progression of a base number layout. Let's look closely at the relationship $y=kx$:

* For B: $60=4\times 15$
* For D: $20=4\times 5$
If the core rule is that the second number is a multiple of the first, both B and D follow $y=4x$.
Let's check the ratio of terms:
* $\text{LCM}(10,15)=30$
* $\text{LCM}(15,60)=60$
* $\text{LCM}(9,12)=36$
* $\text{LCM}(5,20)=20$
In options B, C, and D, the numbers have a common highest ratio or common factor distribution. Specifically, $(10,15)$ is the only pair where the difference is a prime number equal to $5$, or $(10,15)$ stands out as the ratio is $2:3$, while $(9,12)$ is $3:4$, and the others are $1:4$. In competitive exams, $(10,15)$ is classified as odd because both are simple consecutive multiples of 5, whereas the others have structural internal multiplication patterns or $(10,15)$ is distinct because the second number is less than double the first, unlike the others where the second number is significantly larger or a multiple.