(i) Let the number of John’s marbles be x.

Therefore, number of Jivanti’s marble = 45 − x

After losing 5 marbles,

Number of John’s marbles = x − 5

Number of Jivanti’s marbles = 45 − x − 5 = 40 − x

Given that the product of their marbles is 124.

∴ (x – 5) (40 – x) = 124

= x² – 45x +324 = 0

= x² – 36x – 9x +324 = 0

= x(x – 36 ) – 9 (x – 36 ) = 0

= (x – 36) (x – 9) = 0

Either x – 36 = 0 or x − 9 = 0

i.e.,

x = 36 or x = 9

If the number of John’s marbles = 36,

Then, number of Jivanti’s marbles = 45 − 36 = 9

If number of John’s marbles = 9,

Then, number of Jivanti’s marbles = 45 − 9 = 36

(ii) Let the number of toys produced be x.

∴ Cost of production of each toy = Rs (55 − x)

It is given that, total production of the toys = Rs 750

∴ x(55 – x) = 750

= x² – 55x+750 = 0

= x² – 25x – 30x+750 = 0

= x(x – 25 ) – 30(x – 25 ) = 0

= (x – 25)(x – 30) = 0

Either x – 25 = 0 or x − 30 = 0

i.e., x = 25 or x = 30

Hence, the number of toys will be either 25 or 30.