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6 times a fraction is greater than its reciprocal by 1. What is the fraction?

6 times a fraction is greater than its reciprocal by 1. What is the fraction? Correct Answer 1/2

Given:

6 times a fraction is greater than its reciprocal by 1

Concept Used:

In this type of question, fraction can be determined by the help of below formula

Formula Used:

If a fraction is in the form (y/z), then its reciprocal is (z/y)

Calculation:

Let the fraction be (y/z), using the above formulae, we get

⇒ 6 × (y/z) = (z/y) + 1

⇒ 6/ (z/y) = (z/y) + 1

⇒ a2 + a – 6 = 0 {a = (z/y)}

⇒ a = 2

∴ Required fraction = y/z = 1/2

Smart Trick

We can find correct answer by using options

1) 6 × (3/2) - (2/3) = 9 - (2/3) = 25/3 ≠ 1

2) 6 × (1/2) - 2 = 3 - 2 = 1

Hence, option 2 is correct.

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