A number satisfies: its one-fifth increased by 5 equals its one-fourth decreased by 5. What is the number?

Introduction / Context:
Here you are given a linear relationship between two different fractions of the same unknown number, with constant adjustments. Problems like this are common in arithmetic reasoning and require careful setup of a simple equation and accurate fraction manipulation.

Given Data / Assumptions:

• Let the number be N.
• N/5 + 5 = N/4 − 5.
• N is real and positive.

Concept / Approach:
Isolate N by moving all N terms to one side and constants to the other. The coefficient of N will involve the difference between 1/4 and 1/5. Solve by multiplying through by the common denominator to avoid fractional clutter.

Step-by-Step Solution:

Verification / Alternative check:
Check: one-fifth of 200 is 40; 40 + 5 = 45. One-fourth of 200 is 50; 50 − 5 = 45. Both sides equal 45, confirming correctness.

Why Other Options Are Wrong:
160, 180, 220, and 240 do not satisfy both sides simultaneously when substituted into the equation.

Common Pitfalls:
Subtracting the wrong way around (1/5 − 1/4) or forgetting to move constants to the other side before combining fractional coefficients.

Final Answer:
200