# Ratio question help: are my answers correct?

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

## 1 Answer

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.