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The sum of a proper fraction and its reciprocal is 61/30. Find the fraction.
- A1/3
- B5/6
- C3/10
- D3/5
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CCommunity
Let the proper fraction be x/y and its reciprocal be y/x
According to the Question
x/y + y/x = 61/30
⇒ (x2 + y2)/xy = 61/30
Dividing numerator and denominator by y2
⇒ (x2/y2 + 1)/(xy/y2) = 61/30
Let x/y = a
⇒ (a2 + 1)/a = 61/30
⇒ 30a2 + 30 – 61a = 0
On solving we get
a = 1.2 = 6/5 or, a = 0.83 = 5/6
∴ a = x/y = 5/6
According to the Question
x/y + y/x = 61/30
⇒ (x2 + y2)/xy = 61/30
Dividing numerator and denominator by y2
⇒ (x2/y2 + 1)/(xy/y2) = 61/30
Let x/y = a
⇒ (a2 + 1)/a = 61/30
⇒ 30a2 + 30 – 61a = 0
On solving we get
a = 1.2 = 6/5 or, a = 0.83 = 5/6
∴ a = x/y = 5/6