Question

The L.C.M. of two numbers is 495 and their H.C.F. is 5. If the sum of two numbers is 100 then their difference is ____.

• A. 10
• B. 46
• C. 70
• D. 90
• E. 20

Answer 1

The correct option is A 10

Let the two numbers be $x$ and $(100-x)$
$L.C.M.\times H.C.F.=\text{Product of the numbers}$
$495\times 5=x(100-x)$
or, $x^2-100x+2475=0$
or, $x^2-55x-45x+2475=0$
or, $(x-55)(x-45)=0$
or, $x=45$ or $x=55$
Thus, the numbers are 45 and 55.
When $x=55$, we get $100-x=45$ and vice versa.
Hence, their difference $=55-45=10$