Rafiul has more marbles than Roman and they have 45 marbles together. After losing 5 marbles each, the product of the number of marbles they both have now is 124. How to find out how many marbles they had to start with.

Question: Rafiul has more marbles than Roman and they have 45 marbles together. After losing 5 marbles each, the product of the number of marbles they both have now is 124. How to find out how many marbles they had to start with.

Solution:
Let
The number of marbles Rafiul had be x.
Then the number of marbles Roman had = 45 - x.

The number of marbles left with Rafiul after losing 5 marbles = x - 5
The number of marbles left with Roman after losing 5 marbles = 45 - x - 5 = 40 - x

ATQ,
(x - 5) (40 - x) = 124
⇒ 40x - x² - 200 + 5x = 124
⇒ - x² + 45x - 200 = 124
⇒ x² - 45x + 324 = 0
⇒ x² - 36x - 9x + 324 = 0
⇒ x(x - 36) - 9(x - 36) = 0
⇒ (x - 36)(x - 9) = 0
∴ x = 36 and x = 9

So, the number of marbles Rahul had is 36 and Rohan had is 9.