What is the larger number?

Quantity I. Difference between the two numbers is 21 and LCM and HCF of those numbers are 70 and 7 respectively.

Quantity II. The HCF and LCM of two numbers are 12 and 72 respectively. If the sum of the two numbers is 60.

Quantity I. let the larger number be x ∴ Smaller number = (x-21) ∴ x(x – 21) = 70 × 7 x^{2} - 21x = 490 x^{2} - 21x – 490 = 0 (x-35)(x+14) = 0 ∴ x = 35 Larger number = 35 and Smaller number = 14 Quantity II. Let the larger number be x ∴ Smaller number = 60 – x ∴ x (60-x) = 12 ×72 x^{2} - 60x + 864 = 0 (x-36)(x-24) = 0 ∴ x = 36, 24 Larger number = 36 Smaller number = 24 Hence, Quantity I < Quantity II.

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