The LCM of two numbers is 495 and their HCF is 5. If the difference of the numbers is 10, then the two numbers are:

Correct option is B

Given :

LCM of numbers = 495

HCF of two numbers = 5, Difference of numbers = 10

Formula used:

HCF × LCM = Product of numbers

Solution:

​Suppose the numbers are a and b

Using the formula

ab = 495 × 5

And, a - b = 10, a = 10 + b

Substituting a = 10 + b in the product, 

​$$(10 + b)b = 2475 \\b^2 + 10b = 2475 \\b^2 + 10b - 2475 = 0$$​​

On eliminating the middle term,

​$$b^2 + 55b - 45b - 2475 = 0$$

Upon dismantling,

​$$b(b + 55) - 45(b + 55) = 0 \\(b - 45)(b + 55) = 0 \\\ b - 45 = 0 \implies b = 45 \\\ a = 10 + b = 10 + 45 = 55$$​​