Question

If the sum of two numbers is 55 and the hcf and lcm of these numbers are 5 and 120 respectively, then what are the two numbers?

Answer 1

let one number be x
then, another number will be 55-x

we know that,
hcf×lcm=product of two number
5×120=x×55-x
600=55x-x^2
x^2-55x-600=0
x^2-40x-15x-600=0
x(x-40)-15(x-40)=0
(x-15)(x-40)=0
x=15or x=40
therefore, two number are 15 and 40