Explanation:

- Let the numbers be x and y, with x > y.

- Their difference is 20: x - y = 20

- Their HCF is 20, and LCM is 240.

- The product of two numbers = HCF × LCM, so x × y = 20 × 240 = 4800.

- Now, x = y + 20. Substitute in the product:

(y + 20) × y = 4800

y² + 20y - 4800 = 0

- Solving this quadratic:

y² + 20y - 4800 = 0

Factors of 4800 that differ by 20: y = 60 (since 60 × 80 = 4800).

- Larger number is 80, smaller is 60.

- Option 1: 120 — 120 × 100 = 12,000, which is not the product

- Option 2: 80 — fits all conditions, LCM is 240, HCF is 20, and difference is 20

- Option 3: 70 — does not match, product is not 4800

- Option 4: 60 — this is the smaller number

The correct answer is Option 2: 80