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.Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124 .

From the quadratic equation to find how many marbles they had to start with, if John had x marbles.

A: 36,9

B: 20,25

C: 30,15

D: 27, 18

**Explanation:**

John had x marbles and John and Jivanti together have 45 marbles

Then Jivanti has (45-x) marbles

If they both lost 5 marbles then now,

John has =(x-5) marbles and

Jivanti has =(45-x-5)=(40-x) marbles

By the problem,

(x-5)(40-x)=124

⇒40x-200-x^{2}+5x=124

⇒45x-x^{2}-200=124

⇒x^{2}-45x+200+124=0

⇒x^{2}-45x+324=0

⇒x^{2}-36x-9x+324=0, doing middle term factor

⇒x(x-36)-9(x-36)=0

⇒(x-36)(x-9)=0

We know that if the product of two numbers is zero then at least one of them is zero.

Either, x-36=0x=36

Or, x-9=0x=9

If John has =36 marbles then Jivanti has =45-36=9 marbles

And if John has =9 marbles then Jivanti has =45-9=36 marbles

**Final Answer:**

Hence the correct option is (A).