Over the top (OTT) subscribers of a platform are segregated into three categories: i) Kid, ii) Elder, and iii) Others. Some of the subscribers used one app and the others used multiple apps to access the platform. The figure below shows the percentage of the total number of subscribers in 2023 and 2024 who belong to the ‘Kid’ and ‘Elder’ categories.

The following additional facts are known about the numbers of subscribers:

1. The total number of subscribers increased by 10% from 2023 to 2024.
2. In 2024, 1/2 of the subscribers from the ‘Kid’ category and 2/3 of the subscribers from the ‘Elder’ category use one app.
3. In 2023, the number of subscribers from the ‘Kid’ category who used multiple apps was the same as the number of subscribers from the ‘Elder’ category who used one app.
4. 10,000 subscribers from the ‘Kid’ category used one app and 15,000 subscribers from the ‘Elder’ category used multiple apps in 2023.

What could be the minimum percentage of subscribers who used multiple apps in 2024?

The correct answer is 20.0%.

Step-by-step Explanation:

1. Analyzing the Chart Data:
From the provided bar chart, we can extract the percentages of subscribers belonging to the ‘Kid’ and ‘Elder’ categories for the years 2023 and 2024:
• For the 'Kid' category: 15% of the total subscribers in 2023, and 20% in 2024.
• For the 'Elder' category: 20% of the total subscribers in 2023, and 30% in 2024.

2. Establishing Variables for 2023:
Let the total number of subscribers in 2023 be $T_{2023}$.
From the chart:
• Kid subscribers in 2023 = $0.15T_{2023}$
• Elder subscribers in 2023 = $0.20T_{2023}$

3. Using Facts about 2023 Subscribers:
According to Fact 4:
• Kid subscribers using one app in 2023 = 10,000.
• Elder subscribers using multiple apps in 2023 = 15,000.

Let the number of Kid subscribers who used multiple apps in 2023 be $x$. According to Fact 3, this is equal to the number of Elder subscribers who used one app in 2023.

Thus, we can express the total number of subscribers in each category in 2023 as:
• Total Kid subscribers in 2023:
$$\mathrm{10,000}+x=0.15T_{2023}$$
• Total Elder subscribers in 2023:
$$x+\mathrm{15,000}=0.20T_{2023}$$

4. Solving for the 2023 Total Subscribers:
Subtract the first equation from the second equation:
$$(x+\mathrm{15,000})-(\mathrm{10,000}+x)=0.20T_{2023}-0.15T_{2023}$$
$$\mathrm{5,000}=0.05T_{2023}$$
$$T_{2023}=\frac{\mathrm{5,000}}{0.05}=\mathrm{100,000}$$
Using this to find $x$:
$$\mathrm{10,000}+x=0.15\left(\mathrm{100,000}\right)=\mathrm{15,000}\Rightarrow x=\mathrm{5,000}$$

5. Calculating Subscribers for 2024:
From Fact 1, the total number of subscribers increased by 10% from 2023 to 2024:
$$T_{2024}=1.10T_{2023}=1.10\left(\mathrm{100,000}\right)=\mathrm{110,000}$$
Using the percentages for 2024 from the bar chart:
• Total Kid subscribers in 2024 = $20\%\hspace{0.5em}\text{of}\hspace{0.5em}\mathrm{110,000}=\mathrm{22,000}$
• Total Elder subscribers in 2024 = $30\%\hspace{0.5em}\text{of}\hspace{0.5em}\mathrm{110,000}=\mathrm{33,000}$
• Total Others subscribers in 2024 = $(100\%-20\%-30\%)=50\%\hspace{0.5em}\text{of}\hspace{0.5em}\mathrm{110,000}=\mathrm{55,000}$

6. Analyzing App Usage in 2024:
According to Fact 2, we have:
• For the 'Kid' category: $\frac{1}{2}$ use one app, meaning the remaining $\frac{1}{2}$ use multiple apps.
$$\text{Kid multiple app users}=\frac{1}{2}\times \mathrm{22,000}=\mathrm{11,000}$$
• For the 'Elder' category: $\frac{2}{3}$ use one app, meaning the remaining $\frac{1}{3}$ use multiple apps.
$$\text{Elder multiple app users}=\frac{1}{3}\times \mathrm{33,000}=\mathrm{11,000}$$

7. Finding the Minimum Percentage of Multiple App Users:
To minimize the total number of multiple app users in 2024, we assume that none of the subscribers in the 'Others' category use multiple apps (i.e., Others using multiple apps = 0).

Thus, the minimum number of multiple app users in 2024 is:
$$M_{\text{min}}=\mathrm{11,000}\hspace{0.5em}\left(\text{Kids}\right)+\mathrm{11,000}\hspace{0.5em}\left(\text{Elders}\right)+0\hspace{0.5em}\left(\text{Others}\right)=\mathrm{22,000}$$
The minimum percentage of subscribers who used multiple apps in 2024 is:
$${\text{Percentage}}_{\text{min}}=\frac{\mathrm{22,000}}{\mathrm{110,000}}\times 100\%=20.0\%$$