A positive number x satisfies: when x is increased by 10, the result equals 200 times its reciprocal (that is, x + 10 = 200 * (1 / x)). What is the value of x?

Introduction / Context:
This problem checks comfort with translating a verbal condition into an algebraic equation involving a reciprocal. Once the equation is set, solving a simple quadratic yields the positive value for the number. Such questions are common in aptitude tests and reinforce manipulation of fractions and quadratics.

Given Data / Assumptions:

• The number is positive and denoted by x.
• Condition: x + 10 = 200 * (1 / x).
• We seek the positive solution only, because the prompt specifies a positive number.

Concept / Approach:
Clear the denominator to avoid fractions, then bring terms to one side and factor or use the quadratic formula. The reciprocal relation typically produces a quadratic in x. Choose the root that satisfies the positivity constraint.

Step-by-Step Solution:

Verification / Alternative check:
Check the condition: 10 + 10 = 20 and 200 * (1 / 10) = 20. Both sides match, confirming the result.

Why Other Options Are Wrong:
Values 100, 20, 200, and 5 do not satisfy x + 10 = 200 / x when substituted.

Common Pitfalls:
Forgetting to multiply through by x leads to errors with the reciprocal. Selecting the negative root violates the stated condition that the number is positive.

Final Answer:
10