ssriva2 wrote:

Why are we multiplying things two times(^2)?

Because at the end of each month, each person deposits an amount equal to the number of people. For example, if there are 24 people, each would deposit $24 (or whatever currency the question is asking), meaning a total of 24*24 dollars is deposited. So if you start out with \(n\) people:

> After month 1: (\(n\) x \(n\)) deposited = \(n^2\)

> After month 2: +\(n^2\) deposited

> After month 3: +\(n^2\) deposited

> After month 4: +\(n^2\) deposited

> After month 5: +\(n^2\) deposited

> After month 6: +\(n^2\) deposited

** Here, 1/4 of people leave and you are left with \(\frac{3}{4}n\) people, each depositing \(\frac{3}{4}n\) dollars **

> After month 7: +(\(\frac{3}{4}n\)) x (\(\frac{3}{4}n\)) deposited = \(\frac{9}{16}n^2\)

> After month 8: +\(\frac{9}{16}n^2\) deposited

> After month 9: +\(\frac{9}{16}n^2\) deposited

** Here, 1/3 of the remaining people leave and you are left with \((\frac{2}{3})(\frac{3}{4}n)\) people, each depositing \((\frac{2}{3})(\frac{3}{4}n)\) dollars **

> After month 10: + (\(\frac{2}{3})(\frac{3}{4}n\)) x \((\frac{2}{3})(\frac{3}{4}n)\) = \(\frac{1}{4}n^2\)

> After month 11: +\(\frac{1}{4}n^2\)

> After month 12: +\(\frac{1}{4}n^2\)

Put it all together and for the 12-month period, you get:

\(6(n^2) + 3(\frac{9}{16}n^2) + 3 (\frac{1}{4})n^2 = 4860\)

Finally, solve to get:

\(n=24\)

Answer: B