Let's analyze the question from your image:

• The LCM of two numbers is 22 times their HCF.
• The sum of the LCM and HCF is 5750.
• One number is 220, and we need to find the other number.

Let's solve step-by-step.

1. Let $H$ represent the HCF and $L$ represent the LCM of the two numbers.

2. From the problem, $L = 22H$ (since LCM is 22 times the HCF).

3. The sum of the LCM and HCF is given as 5750: $L + H = 5750$ Substituting $L = 22H$ into this equation: $22H + H = 5750$ $23H = 5750$ Solving for $H$: $H = \frac{5750}{23} = 250$ So, the HCF is 250.

4. Now, we know the LCM is: $L = 22 \times 250 = 5500$

5. Using the relation between LCM, HCF, and the product of two numbers, we have: $\text{LCM} \times \text{HCF} = \text{Product of the two numbers}$ Therefore: $5500 \times 250 = 220 \times \text{Other number}$ Solving for the other number: $\text{Other number} = \frac{5500 \times 250}{220} = 6250$

Thus, the other number is 6250.

Would you like more details on any step, or have any other questions?

Here are 5 questions related to this topic:

1. What is the relation between LCM and HCF of two numbers?
2. How can you verify if a given number is the correct LCM of two numbers?
3. What happens when the HCF of two numbers is 1?
4. Can two numbers have the same LCM and HCF?
5. What is the significance of knowing both the LCM and HCF for two numbers?

Tip: For any two numbers, their product is always equal to the product of their LCM and HCF.