Q. 24.2( 181 Votes )

Solve the problem

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


⇒ x2 – 45x +324 = 0

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


⇒ 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


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

⇒ 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.

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