# Need help with a math question

Math problem
New answer on Apr 28, 2023
227 Views

A software company gets 40 new customers per month, and also loses 40 old customers. On average each customer stays for 3 years. How many customers does this software company have? Thanks!

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Hi there,

Q: A software company gets 40 new customers per month, and also loses 40 old customers. On average each customer stays for 3 years. How many customers does this software company have?

You can check what would happen after year 3, when the company starts to lose customers:

• End of Y1: 40*12 = 480 (no lost customers as it starts after year 3)
• End of Y2: 40*12+480 = 960 (no lost customers as it starts after year 3)
• End of Y3: 40*12+960= 1440 (no lost customers as it starts after year 3)
• End of Y4: 40*12+1440-40*12 = 1440 (lost customers present as we are after year 3)
• End of Y5 and onwards: same as Y4

Best,

Francesco

Hi there,

I think this is an interesting question that may be relevant for many people. I would be happy to share my thoughts on it:

• First of all, the correct answer is 1,440:
Y1: 40 * 12 = 480
Y2: 40 * 12 + 480 = 960
Y3: 40 * 12 + 960 = 1,440
Y4: 40 * 12 + 1,440 - 40 * 12 = 1,440 aso.
• Moreover, while this might be an interesting mathematical question, please keep in mind that strategy consulting companies normally do not ask such brain teasers or logic questions in the interviews.

If you would like a more detailed discussion on how to best prepare for your upcoming interviews, please don't hesitate to contact me directly.

Best,

Hagen

The company has “3 years of customers”.

40 customers * 12 months * 3 years =1440 customers

Hi there,

key here is to account for the initial ramp up, where no attrition happens yet.

• Y1: 40 new customers x 12 months = 480 customers
• Y2: 40 new customers x 12 months = 480 customers → 960 customers in total
• Y3: 40 new customers x 12 months = 480 customers → 1440 customers in total
• Y4: 40 new customers x 12 months - 40 old customers x 12 months = 0 → 1440 customers in total
• Y5+: same as year 4

This means that after Year 3 you reach steady state of 1440 customers in total, as the net of inflows and outflows becomes 0.

Hope this helps.

Regards, Andi

(edited)

To calculate the total number of customers, we first need to find the number of customers gained and lost per year.

New customers per year: 40 (new customers per month) * 12 (months per year) = 480

Since the company loses the same number of customers as it gains, the company also loses 480 customers per year.

Since each customer stays for 3 years, the company maintains a consistent number of customers throughout this period. Therefore, the total number of customers will be the number of new customers gained over a 3-year period:

Total customers: 480 (new customers per year) * 3 (years) = 1,440

The software company has a total of 1,440 customers.

Hi there!

To calculate how many customers the software company has, we need to consider the net gain or loss of customers each month, and how long they stay on average.

In this case, the company gains 40 new customers and loses 40 old customers every month, so their net gain/loss is zero. However, we know that each customer stays for an average of 3 years, which means that the total number of customers is the number of new customers gained each month times the average length of time they stay.

So, to calculate the total number of customers, we can multiply the number of new customers gained each month (40) by the number of months they stay on average (36, which is 3 years in months):

40 * 36 = 1440

Therefore, the software company has 1440 customers.

Hope that helps!

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