Question

Two numbers L.C.M is 495 and H.C.F is 5 If the sum of two numbers is 100, then what is the Subtraction of two numbers?

Answer 1

Hiii friend,

Let the numbers be X and Y .

According to question,


X + Y = 100........(1)


HCF of two numbers = 5

And,

LCM of two numbers = 495

we know that,

Product of two numbers = HCF × LCM

X × Y = 5 × 495

XY = 2475......(2)



From equation 1 we get,

X + Y = 100

X = 100-Y......(3)


Putting the value of X in equation (2)

X × Y => 2475

(100-Y) × Y = 2475

100Y - Y² = 2475


Y²-100Y+2475 = 0

Y²-55Y-45Y+2475 => 0


Y(Y-55) -45(Y-55) => 0

(Y-55) (Y-45)=> 0

(Y-55) => 0 OR (Y-45) => 0

Y = 55 OT Y = 45.

Therefore,

Two numbers are 55 and 45.

Therefore,

X - Y => 55-45 => 10.

HENCE,

THE SUBTRACTION OF TWO NUMBERS IS 10.



HOPE IT WILL HELP YOU.... :-)