Solve :

John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with.

Let initially John had x marbles, so Jivanti had (45 - x) marbles.

After loosing 5 marbles by each of them, they have :

John = (x - 5), Jivanti = (45 - x - 5) = (40 - x).

Given,

Product of marbles they now have is 124.

∴ (x - 5)(40 - x) = 124

⇒ 40x - x² - 200 + 5x = 124

⇒ 45x - x² - 200 - 124 = 0

⇒ 45x - x² - 324 = 0

⇒ x² - 45x + 324 = 0

⇒ x² - 9x - 36x + 324 = 0

⇒ x(x - 9) - 36(x - 9) = 0

⇒ (x - 36)(x - 9) = 0

⇒ x - 36 = 0 or x - 9 = 0

⇒ x = 36 or x = 9.

Hence, initially they start with 9 and 36 marbles.