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Answer: Option A : 1489, 11Solution:
Concept:
HCF : The sum of any two numbers is divisible by their HCF. Product of two numbers = HCF × LCMGiven:
Sum of two numbers = 1500 LCM = 16379Calculation:
1500 = 22 × 3 × 53
16379 = 11 × 1489 Clearly, The HCF (h) of 1500 and 16379 is 1. As we know, a × (1500 - a) = HCF × LCM = 1 × 16379⇒ 1500a - a2 = 16379
⇒ a2 - 1500a - 16379 = 0
⇒ a2 - 1489a - 11a - 16379 = 0 ⇒ a (a - 1489) - 11(a - 1489) = 0 ⇒ (a - 11) ( a - 1489) = 0 ⇒ a = 11, 1489 For a = 11, b = 1500 - 11 = 1489 For a = 1489, b = 1500 - 1489 = 11
∴ In both the cases, two numbers are 11 and 1489.