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

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

A 46

B 70

C 10

D 90

Solution

Correct Answer: Option C

Let the numbers be x and (100-x).

Then \(x\left(100-x\right)=5\times495\)

= \(x^2-100x+2475=0\)

=> (x-55) (x-45) = 0

=> x = 55 or x = 45

The numbers are 45 and 55

Required difference = (55-45) = 10