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 a bar graph representing 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 number of subscribers.
- The total number of subscribers increased by 10% from 2023 to 2024.
- In 2024, 1/2 of the subscribers from the ‘Kid' category and 2/3 of the subscribers from the 'Elder' category subscribers use one app.
- 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.
- 10,000 subscribers from the 'Kid' category used one app and 15,000 subscribers from the 'Elder' category used multiple apps in 2023.
Solution
| Year | Kids | Elders | Others |
|---|---|---|---|
| 2023 | 15% | 20% | 65% |
| 2024 | 20% | 30% | 50% |
Reading the bar graphs, we can make the above table.
| Category | 2023 | 2024 |
|---|---|---|
| Kid | 15% = 0.15x | 20% = 0.22x |
| Elders | 20% = 0.2x | 30% = 0.33x |
| Others | 65% = 0.65x | 50% = 0.55x |
| Total | x | 1.1x |
Using clue 1:
The total number of subscribers increased by 10% from 2023 to 2024.
Let the total number of subscribers in 2023 be x.
Therefore, the total number of subscribers in 2024 will be x * 110% = 1.1x.
| Category | 2023 | 2024 |
|---|---|---|
| Kid | 0.15x | 0.22x |
| Elders | 0.2x | 0.33x |
| Others | 0.65x | 0.55x |
| Total | x | 1.1x |
| Category | 2023 (One) | 2023 (Multi) | 2024 (One) | 2024 (Multi) |
|---|---|---|---|---|
| Kid | 0.11x | 0.11x | ||
| Elders | 0.22x | 0.11x | ||
| Others | ||||
| Total |
Using clue 2:
In 2024, half of the subscribers from the 'Kid' category and two-thirds of the subscribers from the 'Elder' category use one app.
Therefore, half of 0.22x = 0.11x and two-thirds of 0.33x = 0.22x used one app.
So, kids using multiple apps = 0.22x - 0.11x = 0.11x
and elders using multiple apps = 0.33x - 0.22x = 0.11x.
| Category | 2023 | 2024 |
|---|---|---|
| Kid | 0.15x | 0.22x |
| Elders | 0.2x | 0.33x |
| Others | 0.65x | 0.55x |
| Total | x | 1.1x |
| Category | 2023 (One) | 2023 (Multi) | 2024 (One) | 2024 (Multi) |
|---|---|---|---|---|
| Kid | y | 0.11x | 0.11x | |
| Elders | y | 0.22x | 0.11x | |
| Others | ||||
| Total |
Using clue 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.
Let that number be "y".
| Category | 2023 | 2024 |
|---|---|---|
| Kid | 0.15x | 0.22x |
| Elders | 0.2x | 0.33x |
| Others | 0.65x | 0.55x |
| Total | x | 1.1x |
| Category | 2023 (One) | 2023 (Multi) | 2024 (One) | 2024 (Multi) |
|---|---|---|---|---|
| Kid | 10000 | y | 0.11x | 0.11x |
| Elders | y | 15000 | 0.22x | 0.11x |
| Others | ||||
| Total |
Using clue 4:
10,000 subscribers from the 'Kid' category used one app and 15,000 subscribers from the 'Elder' category used multiple apps in 2023.
| Category | 2023 | 2024 |
|---|---|---|
| Kid | 0.15x | 0.22x |
| Elders | 0.2x | 0.33x |
| Others | 0.65x | 0.55x |
| Total | x | 1.1x |
| Category | 2023 (One) | 2023 (Multi) | 2024 (One) | 2024 (Multi) |
|---|---|---|---|---|
| Kid | 10000 | y | 0.11x | 0.11x |
| Elders | y | 15000 | 0.22x | 0.11x |
| Others | ||||
| Total |
Using both tables, we can make the following two equations:
10000 + y = 0.15x ...(1)
and y + 15000 = 0.2x ...(2)
Solving both equations, we get:
x = 100000 and y = 5000
Substituting the x and y values in the table, we get:
| Category | 2023 | 2024 |
|---|---|---|
| Kid | 15000 | 22000 |
| Elders | 20000 | 33000 |
| Others | 65000 | 55000 |
| Total | 100000 | 110000 |
| Category | 2023 (One) | 2023 (Multi) | 2024 (One) | 2024 (Multi) |
|---|---|---|---|---|
| Kid | 10000 | 5000 | 11000 | 11000 |
| Elders | 5000 | 15000 | 22000 | 11000 |
| Others | ||||
| Total |
Since we know the values of x and y, we can convert the percentages to numbers.
In 2023, total subscribers in Kid category = 0.15x = 15000
In 2023, total subscribers in Kid category using one app = 10000
In 2023, total subscribers in Kid category using multiple apps = y = 15000 - 10000 = 5000
| 2023 | 2024 | |
|---|---|---|
| KID | ||
| ELDER | ||
| OTHERS | ||
| TOTAL |
| 2023 (One app) | 2023 (Multiple apps) | 2024 (One app) | 2024 (Multiple apps) | |
|---|---|---|---|---|
| KID | ||||
| ELDER | ||||
| OTHERS | ||||
| TOTAL |
Percentage increase in the number of subscribers in the Elder category from to