Question

The L.C.M of two numbers is 495 and their H.C.F is 5. If the sum of the numbers is 100, then their difference is ?​

Answer 1

Answer:

hi

your answer is here !

Step-by-step explanation:

$Let the numbers be x and (100-x).</p><p></p><p> </p><p></p><p>Then,x(100−x)=5*495x100-x=5*495</p><p></p><p> </p><p></p><p> =>  x2−100x+2475=0x2-100x+2475=0</p><p></p><p> </p><p></p><p> =>  (x-55) (x-45) = 0</p><p></p><p> </p><p></p><p> =>  x = 55 or x = 45</p><p></p><p> </p><p></p><p>  The numbers are 45 and 55</p><p></p><p> </p><p></p><p>Required difference = (55-45) = 10</p><p></p><p>$

Answer 2

Answer:

two no.’s are 45 and 55

Step-by-step

Let the two numbers be a and b respectively

As per the given data,

LCM = 495

HCF =5

As per a calculation in mathematics,

The product of HCF and LCM calculated for two numbers is equal to the product of two numbers themselves

LCM * HCF = a * b

Thus,

495 * 5 = ab

2475 = ab …1

Now, it is stated that,

a + b = 10 0

Thus, b = 100- a… 2

Put 2 in 1, we have,

2475 = a(100 - a)

Which gives us,

2475 = - a^2 + 100a

On rearranging, we get,

a^2 - 100a + 2475 = 0

a²-55a-45a+2475=0

a(a-55)-45(a-55)=0

(a-45)(a-55)=0

a=45,55

b=55,45

two no.’s are 45 and 55