If the sum of two numbers is 80 and the HCF and LCM of these numbers are 20 and 60, then the sum of their reciprocals is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\frac{1}{15}\)
For any two numbers, HCF × LCM = the product of the numbers. The sum of the reciprocals of \(a\) and \(b\) is \(\frac{1}{a}+\frac{1}{b}=\frac{a+b}{ab}\), so only the sum and the product are needed.
Product of the numbers \(=20\times60=1200\)
Sum of the reciprocals \(\displaystyle =\frac{80}{1200}=\frac{1}{15}\)