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Deconstructing the Question

The 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-step

Let 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)
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