**Solution:**

**(i)** Let the breadth = x metres

Length = 2 (Breadth) + 1

Length = (2x + 1) metres

Since Length × Breadth = Area

∴ (2x + 1) × x = 528

2x^{2} + x = 528

2x^{2} + x – 528 = 0

Thus, the required quadratic equation is

**2x**^{2} + x – 528 = 0

**(ii)** Let the two consecutive numbers be x and (x + 1).

∵ Product of the numbers = 306

∴ x (x + 1) = 306

⇒ x^{2} + x = 306

⇒ x^{2} + x – 306 = 0

Thus, the required equdratic equation is

**x**^{2} + x – 306 = 0

**(iii) **Let the present age = x

∴ Mother’s age = (x + 26) years

After 3 years

His age = (x + 3) years

Mother’s age = [(x + 26) + 3] years

= (x + 29) years

According to the condition,

⇒ (x + 3) × (x + 29) = 360

⇒ x^{2} + 29x + 3x + 87 = 360

⇒ x^{2} + 29x + 3x + 87 – 360 = 0

⇒ x^{2} + 32x – 273 = 0

Thus, the required quadratic equation is

**x**^{2} + 32x – 273 = 0

**(iv)** Let the speed of the tram = u km/hr

Distance covered = 480 km

Time taken = Distance + Speed

= (480 ÷ u) hours

**= 480/u hours**

**In second case,**

Speed = (u – 8) km/ hour

According to the condition,

⇒ 480u – 480(u – 8) = 3u(u – 8)

⇒ 480u – 480u + 3840 = 3u^{2} – 24u

⇒ 3840 – 3u^{2} + 24u = 0

⇒ 1280 – u^{2} + 8u = 0

⇒ –1280 + u^{2} – 8u = 0

⇒ u^{2} – 8u – 1280 = 0

Thus, the required quadratic equation is

** u**^{2} – 8u – 1280 = 0