he LCM of two numbers is 4 times their HCF. The sum of the LCM and HCF is 125. If one of the numbers is 100, what is the other number?

Let HCF = $x$

Then LCM = $4x$

Given:
$x + 4x = 125$
$5x = 125 \Rightarrow x = 25$

So, HCF = 25 and LCM = $4 \times 25 = 100$

Use relation:
Product of numbers = HCF × LCM

$100 \times \text{other number} = 25 \times 100$

Other number = $\frac{2500}{100} = 25$

✅ Final Answer: 25