Question

The sum of a fraction and its reciprocal is \(2 \frac{25}{66}\). The greater of the two numbers is-
1. \(1 \frac{15}{22}\)
2. \(1 \frac{5}{6}\)
3. \(1 \frac{20}{33}\)
4. \(1 \frac{5}{11}\)

Answer 1

Correct Answer - Option 2 : \(1 \frac{5}{6}\)

Given:

The sum of a fraction and its reciprocal is \(2 \frac{25}{66}\)

Calculation:

Let the fraction be (x/y) (Denote this by ‘a’)

Sum of the fraction (a) and its reciprocal (1/a) = \(2 \frac{25}{66}\)

a + (1/a) = 157/66

⇒ (a² + 1)/a = 157/66

⇒ 66a² - 157a + 66 = 0

⇒ 66a² - 121a - 36a + 66 = 0

⇒ 11a(6a - 11) - 6(6a - 11) = 0

⇒ (11a - 6) (6a - 11) = 0

⇒ a = 11/6 or 6/11

Greater is 11/6 = \(1 \frac{5}{6}\)

∴ Required answer is \(1 \frac{5}{6}\)