Question

The LCM of the two numbers is 495 and their HCF is 5.if the sum of the number is 100.then their difference is

Answer 1

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

Thus, b = 10 - a… 2

Put 2 in 1, we have,

2475 = a(10 - a)

Which gives us,

2475 = - a^2 + 10a

On rearranging, we get,

a^2 - 10a + 2475 = 0

Using the formula method

B^2 - 4AC

Here B=-10, A=1 C=2475

(-10)^2 - 4(1)(2475)

= 100 - 4(2475)

= - 9800…which is less than 0

Thus, there exists no factors for equation

a^2 - 10a + 2475 = 0

Which implies no value of ‘a’ exists which satisfies the mentioned quadratic equation

As per 2, b depends on a, and hence as a does not exist, b also does not exist.

Conclusion : There does not exist any two numbers for which LCM is 495, HCF is 5 and their sum is 10.

Answer 2

Answer:

10

Step-by-step explanation:

Let the two numbers be a and b respectively

As per the given data,LCM = 495HCF =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

Thus, b = 10 - a… 2

Put 2 in 1, we have,2475 = a(10 - a)

Which gives us,2475 = - a^2 + 10a

On rearranging, we get,a^2 - 10a + 2475 = 0

a^2-10a+2475=0

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

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

a=55 or a=45s

so, difference of two number  is 55-45=10

now the answer is 10