Question:
The LCM of two numbers is 9 times their HCF. The sum of LCM and HCF is 500. Find their HCF.
Solution:
Let the HCF of two numbers be x.
Then, LCM = 9x
According to the question,
$\mathrm{LCM}+\mathrm{HCF}=500$
$\Rightarrow 9 x+x=500$
$\Rightarrow 10 x=500$
$\Rightarrow x=50$
Hence, the HCF of two numbers is 50.
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