Deconstructing the QuestionThe investment increases by
x% in January and decreases by
y% in February.
The final value equals the original value.
We must find
y in terms of
x.
Step-by-stepLet the initial value be
1.
After January:
\(1 \times \left(1 + \frac{x}{100}\right)\)
After February:
\(\left(1 + \frac{x}{100}\right)\left(1 - \frac{y}{100}\right) = 1\)
Expand:
\(1 + \frac{x}{100} - \frac{y}{100} - \frac{xy}{10000} = 1\)
Subtract 1:
\(\frac{x}{100} - \frac{y}{100} - \frac{xy}{10000} = 0\)
Multiply by 10000:
\(100x - 100y - xy = 0\)
Rearrange:
\(100x = y(100 + x)\)
Solve:
\(y = \frac{100x}{100 + x}\)
Answer: 100x / (100 + x)