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Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?
  • a)
    4/5
  • b)
    9/4
  • c)
    4/9
  • d)
    5/4
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Sum of a fraction and thrice of its reciprocal is 73/20. What is the f...
Let the fraction be x.
Reciprocal = 1/x
Then,
x + 3/x = 73/20
⇒ x2 + 3 = 73x/20
⇒ 20x2 – 73x + 60 = 0
⇒ x = {- (-73) + √ (5329 – 4800)}/40     or        x = {- (-73) - √ (5329 – 4800)}/40
⇒ x = 96/40 = 12/5                                or        x = 50/40 = 5/4
∴ the required fraction is 5/4 or 12/5.
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Most Upvoted Answer
Sum of a fraction and thrice of its reciprocal is 73/20. What is the f...
To solve this problem, let's assume the fraction as x/y, where x and y are positive integers.

According to the given information, the sum of the fraction and thrice of its reciprocal is 73/20:

(x/y) + 3(y/x) = 73/20

To simplify this equation, let's get rid of the fractions by multiplying both sides by xy:

xy(x/y) + 3xy(y/x) = 73/20 * xy

This simplifies to:

x^2 + 3y^2 = 73/20 * xy

Now, let's multiply both sides by 20 to get rid of the fraction:

20x^2 + 60y^2 = 73xy

Next, let's rearrange the equation to get it in a quadratic form:

20x^2 - 73xy + 60y^2 = 0

This equation can be factored as:

(5x - 12y)(4x - 5y) = 0

Now we have two possible solutions:

1) 5x - 12y = 0
2) 4x - 5y = 0

Let's solve these two equations separately:

1) 5x - 12y = 0
Rearranging, we get:
5x = 12y
x/y = 12/5

2) 4x - 5y = 0
Rearranging, we get:
4x = 5y
x/y = 5/4

So, the possible fractions are x/y = 12/5 and x/y = 5/4.

However, the question asks for the fraction, not the ratio. Therefore, the correct answer is x/y = 5/4, which is option D.
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Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?a)4/5b)9/4c)4/9d)5/4Correct answer is option 'D'. Can you explain this answer?
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