Solutions:

Let us say, the number of marbles Sulav have = *x*.

Therefore, the number of marbles Sukriti have = 45 – *x*

After losing 5 marbles each,

Number of marbles Sulav's have = *x* – 5

Number of marble Sukriti's have = 45 – *x* – 5 = 40 –* x*

Given that the product of their marbles is 124.

∴ (*x *– 5)(40 – *x*) = 124

⇒ *x*^{2} – 45*x* + 324 = 0

⇒ *x*^{2} – 36*x* – 9*x* + 324 = 0

⇒ *x*(*x* – 36) -9(*x* – 36) = 0

⇒ (*x* – 36)(*x* – 9) = 0

Thus, we can say,

*x* – 36 = 0 or *x* – 9 = 0

⇒ *x* = 36 or *x* = 9

*Therefore,*

If, Sulav’s marbles = 36,

Then, Sukriti's marbles = 45 – 36 = 9

And if Sulav’s marbles = 9,

Then, Sukriti's marbles = 45 – 9 = 36

∴ Sulav had to start with 9 marbles and Sukriti had to start with 36 marbles.