The active subscriber count of a streaming platform in 2021 was 20,000. If the count increased by 20% in 2022, decreased by 15% in 2023, and increased by $X$% in 2024 to reach 25,500, then determine the value of $X$.

The correct option is 25.

Step 1: Calculate the subscriber count at the end of 2022.

The active subscriber count in 2021 was 20,000.

In 2022, the subscriber count increased by 20%.

$\text{Subscriber count in 2022}=\mathrm{20,000}\times \left(1+\frac{20}{100}\right)$

$=\mathrm{20,000}\times 1.20$

$=\mathrm{24,000}$

Step 2: Calculate the subscriber count at the end of 2023.

In 2023, the subscriber count decreased by 15%.

$\text{Subscriber count in 2023}=\mathrm{24,000}\times \left(1-\frac{15}{100}\right)$

$=\mathrm{24,000}\times 0.85$

$=\mathrm{20,400}$

Step 3: Determine the percentage increase $X$ in 2024.

In 2024, the subscriber count increased by $X$% to reach 25,500.

$\text{Subscriber count in 2024}=\mathrm{20,400}\times \left(1+\frac{X}{100}\right)=\mathrm{25,500}$

$1+\frac{X}{100}=\frac{\mathrm{25,500}}{\mathrm{20,400}}$

$1+\frac{X}{100}=1.25$

$\frac{X}{100}=1.25-1$

$\frac{X}{100}=0.25$

$X=25$

Therefore, the value of $X$ is 25.