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From the question given below, I am trying to, firstly, find the proportion of iPhone users from the information provided in the Business Scenario.

Secondly, I am trying to find the share of Android logins given the updated information.

For these questions, I didn't see the importance of the total average logins of 15 or 18 (for part 2) and so I just used the information of the iPhone logins and Android logins. I wasn't sure how/whether I needed to use the information from the overall average logins?

Therefore, for the first part, my calculation was $$\text{proportion} = \frac{9}{9+19} * 1000000 = 321.429 $$

For part 2 I got 56% using the following calculation $$\frac{19}{15+19} $$

Are these answers correct?

Question

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Check calculations

Initial Scenario : 1 M Users with 15 login/month average.

This means : 15 M logins in a month.

Average number of login per month : 9 for iPhone Users and 19 for Android Users.

The equation will be : $19 \times \text A + 9 \times (1 - \text A) = 15$, where $\text A$ is the number of Android Users and $\text {iP} = 1 - \text A$ is the number of iPhone Users.

Solving, we get : $10 \times \text A =6$, and thus $\text A=0,6$.

In conclusion, the Initial Scenario is : 600 K Android Users and 400 K iPhone Users.


Final Scenario : in the final scenario the number of logins is increased by 20%, and thus amounts to 18 M logins ($15 \times 1.2$).

iPhone logins increase by $\dfrac 2 3$ , i.e. from 9 to 15.

The new equation will be : $0,6 \times y + 15 \times 0,4 = 18$, where $y$ is the new average number of logins of Android Users.

Solving for $y$, we get $y=20$, that is the new number of logins per month of Android Users.


Conclusion

Initial Scenario : average number of login per month : 9 for iPhone Users and 19 for Android Users.

Final Scenario : average number of login per month : 15 for iPhone Users and 20 for Android Users.

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