Answer :

(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

⇒ x^{2} – 45x +324 = 0

Now, to factorize this equation, we need to take numbers such that their product is 324 and sum is 45

⇒ x^{2} – 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

⇒ x^{2} – 55x + 750 = 0

Now to factorize this equation we have to find two numbers such that their product is 750 and sum is 55

⇒ x^{2} – 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.

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