A $20\%$ increase means multiply the marketing allocation by $1.20$. A $p\%$ decrease means multiply the manufacturing allocation by $1-\frac{p}{100}$.

The 2025 total is $1.02T$. Set the sum of the two changed category allocations equal to this amount.

Algebra is the fastest method because the category percentages give a direct linear equation in $p$. Desmos can verify the result.

Enter $y=0.42+0.65(1-x/100)$ and $y=1.02$. Here, $x$ represents the percentage decrease in manufacturing.

Click the intersection of the two graphs. Its $x$-coordinate is the value of $p$. Enter $100/13$ on a separate expression line to verify that its decimal value matches the intersection's $x$-coordinate.

Let the total 2024 operating budget be $T$.

The 2024 marketing allocation was $0.35T$, and the manufacturing allocation was $0.65T$.

The 2025 marketing allocation was $1.20(0.35T)=0.42T$.

The 2025 manufacturing allocation was $0.65\left(1-\frac{p}{100}\right)T$.

Since the total 2025 budget was $2\%$ greater than $T$, it was $1.02T$. Therefore,

Subtract $1.02$ from $1.07$:

Thus,