Ram and Shyam had together have 45 marbles. Both of them lost 5 marbles each. The product of the number of marbles they now have is 124. Write a quadratic equation to represent this problem mathematically.

The correct answer is $-x^2+45x-324=0$

Let the number of marbles Ram had be x.
∴ Number of marbles Shyam had = (45 - x)
After losing 5 marbles,
Number of marbles left with Ram = x - 5
and number of marbles left with Shyam = 45 - x - 5 = 40 - x
Since their product is 124,
(x - 5)(40 - x) = 124
-x² + 40x + 5x - 200 = 124
-x² + 45x - 324 = 0