Question
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. Study the following information carefully and answer the Questions given below:Solution
Quantity I. let the larger number be x ∴ Smaller number = (x-21) ∴ x(x – 21) = 70 × 7 x2 - 21x = 490 x2 - 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 x2 - 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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