Question

The LCM and HCF of two positive numbers are 175 and 5 respectively If the sum of the numbers is 60 what is the difference between them ?

Answer 1

Given,
The LCM and HCF of two positive numbers are $175$ and $5$ respectively.
Let the two numbers be $5a$ and $5b$ as HCF of the two numbers = $5$
$\therefore$ The product of the two numbers = HCF $\times$ LCM
$5a\times 5b=5\times 175$
$\therefore ab=\frac{175}{5}=35$
$(a,b)$ can be $(1,35)$ or $(5,7)$
Thus the numbers can be $(1\times 5$ and $35\times 5)$=$(5$ and $175)$
or $(5\times 5$ and $5\times 7)$= $(25$ and $35)$
The sum = $60$ is satisfied by the pair $(25,35)$
Hence the difference of the numbers is $35-25=10$