1. The problem asks us to find multiples of given numbers that lie between 85 and 110. 2. A multiple of a number $n$ is any number that can be expressed as $n \times k$ where $k$ is an integer. 3. For the number 50, the multiple given is 100, which is $50 \times 2$ and lies between 85 and 110. 4. For 45, we need to find an integer $k$ such that $85 \leq 45k \leq 110$. 5. Dividing the inequalities by 45, we get: $$\frac{85}{45} \leq k \leq \frac{110}{45}$$ $$1.888\ldots \leq k \leq 2.444\ldots$$ 6. Since $k$ must be an integer, $k=2$ is the only integer in this range. 7. So, the multiple of 45 is: $$45 \times 2 = 90$$ 8. For 27, similarly, find $k$ such that: $$85 \leq 27k \leq 110$$ 9. Dividing by 27: $$\frac{85}{27} \leq k \leq \frac{110}{27}$$ $$3.148\ldots \leq k \leq 4.074\ldots$$ 10. The integers in this range are $k=4$. 11. So, the multiple of 27 is: $$27 \times 4 = 108$$ 12. Final answers: - Multiple of 45 between 85 and 110 is 90. - Multiple of 27 between 85 and 110 is 108.