A fraction is greater than its reciprocal by 9/20. What is the value of the fraction?

Introduction / Context:
This question uses a relationship between a fraction and its reciprocal. Such problems are common in algebra sections of aptitude tests, because they require forming and solving an equation.

Given Data / Assumptions:

• Let the fraction be x.
• Its reciprocal is 1/x, with x not equal to 0.
• We are told that x is greater than 1/x by 9/20, so x - 1/x = 9/20.
• We need to find x from the given options.

Concept / Approach:
Translate the statement into an algebraic equation, clear the denominator and solve the resulting quadratic equation. Then match the solutions with the choices and consider which value is appropriate as a fraction in this context.

Step-by-Step Solution:

Verification / Alternative check:
Check x = 5/4: 5/4 - 4/5 = (25 - 16) / 20 = 9/20, which satisfies the equation. Check x = -4/5: -4/5 - (-5/4) also equals 9/20, but this gives a negative fraction while the context and options suggest a positive fraction.

Why Other Options Are Wrong:
4/5 and 3/4 are less than 1 and therefore cannot be greater than their reciprocals. 4/3 is greater than 1, but substituting x = 4/3 does not give a difference of 9/20. Only 5/4 satisfies the given relationship.

Common Pitfalls:
Many students forget that the equation may produce two solutions, one positive and one negative. They may also make algebraic mistakes when multiplying by the common denominator or in computing the discriminant. Always check candidate solutions in the original equation.

Final Answer:
The required fraction is 5/4.