Question

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

Answer 1

We have to determine the difference of the numbers

We know that

$$\begin{gathered} L.C.M.\times H.C.F.=Productofthenumbers \\ 495\times 5=x(100-x) \\ =>x^2-100x+2475=0 \\ =>x^2-55x-45x+2475=0 \\ =>(x-55)(x-45)=0 \\ =>x=45orx=55 \end{gathered}$$

So the two numbers are, $45$ and$55$

Now, the difference $=55-45=10$

Therefore, the difference between two numbers is $10.$