The L.C.M of two numbers is 495 and their H.C.F is 5. If the sum of the  number is 100, then their difference is- 1 point10467090

The problem is asking for the difference between two numbers given their Least Common Multiple (LCM), Highest Common Factor (HCF), and their sum.

Here are the steps to solve the problem:

1. We know that the product of two numbers is equal to the product of their LCM and HCF. So, let's denote the two numbers as a and b. We have:

   a * b = LCM * HCF a * b = 495 * 5 a * b = 2475

2. We also know that the sum of the two numbers is 100. So, we have:

   a + b = 100

3. Now, we have a system of two equations, and we can solve it to find the values of a and b.

   From the second equation, we can express b as b = 100 - a.

   Substituting this into the first equation gives:

   a * (100 - a) = 2475 100a - a^2 = 2475 a^2 - 100a + 2475 = 0

4. This is a quadratic equation, and we can solve it using the quadratic formula:

   a = [100 ± sqrt((100)^2 - 412475)] / (2*1) a = [100 ± sqrt(10000 - 9900)] / 2 a = [100 ± sqrt(100)] / 2 a = [100 ± 10] / 2 a = 45 or 55

5. So, the two numbers are 45 and 55. Their difference is:

   |55 - 45| = 10

So, the difference between the two numbers is 10.