Jiya, Kavya, Shivam, and Mani start walking from the same point in the same direction around a rectangular track and each one of them completes one round in 180 seconds, 270 seconds, 360 seconds, and 450 seconds respectively. After how much time will they all meet again at one point?

I. x² - 33x + 270 = 0

II. y² - 41y + 414 = 0

I. 20x² - 93x + 108 = 0

II.72y² - 47y - 144 = 0

I. 8y²- 2y - 21 = 0

II. 2x²+ x - 6 = 0

I. 27(p + 2) = 2p(24 – p)

II. 2q² – 25q + 78 = 0

I. 6p² + 17p + 12 = 0

II. 12q² - 25q + 7 = 0

I. 7x + 8y = 36

II. 3x + 4y = 14

I. 64x² - 64x + 15  = 0     

II. 21y² - 13y + 2  =0

I. x² - 19x + 84 = 0

II. y² - 25y + 156 = 0

1.3wx = 40 – wy

2. b² = 2b + p

3. d² + d = q

Now, observe the given conditions:

I. 22x² - 97x + 105 = 0

II. 35y² - 61y + 24 = 0