Two numbers have a sum of 55, with their highest common factor (HCF) being 5 and their least common multiple (LCM) being 120. What is the value of the sum of their reciprocals?

Explanation

Let the two numbers be a and b. Given a + b = 55 and their HCF × LCM = a × b = 5 × 120 = 600. The sum of their reciprocals is 1/a + 1/b = (a + b) / (ab) = 55 / 600, which simplifies to 11 / 120.