Answer :
The difference of the numbers would be equal to C. 10.
The product of two numbers is equal to the product of their LCM and HCF. So, we have:
[tex]\[a \times b = \text{LCM} \times \text{HCF}\]\[a \times b = 495 \times 5\]\[a \times b = 2475\][/tex]
We also know that the sum of the two numbers is 100. So, we have:
a + b = 100
System of equations:
1. a x b = 2475
2. a + b = 100
Solve this system of equations to find the values of a and b.
We know that:
[tex]\[ (a + b)^2 = a^2 + b^2 + 2ab \][/tex]
Substituting the given values:
[tex]\[ (100)^2 = a^2 + b^2 + 2(2475) \]\[ 10000 = a^2 + b^2 + 4950 \]\[ a^2 + b^2 = 10000 - 4950 \]\[ a^2 + b^2 = 5050 \][/tex]
Now, we know that:
[tex]\[ (a - b)^2 = a^2 + b^2 - 2ab \][/tex]
Substituting the known values:
[tex]\[ (a - b)^2 = 5050 - 2(2475) \]\[ (a - b)^2 = 5050 - 4950 \]\[ (a - b)^2 = 100 \][/tex]
Taking the square root of both sides:
[tex]\[ a - b = \sqrt{100} \]\[ a - b = 10 \][/tex]
The difference between the two numbers is 10.