Some people form a joint account for one year with the condition that

Solution

• Every month each member deposits an amount equal to the number of members in the account in that month
• The person who withdraws from the account before the end of the year gets his/her amount at the end of the year.
• After 6 months, 1/4th of the people withdraw and 1/3rd of the remaining withdraw after 3 months.
• Of the monsters who can spit fireballs, 8 also blow freezing wind.
• At the end of the year, there is an amount of Rs. 4860 in the account before paying off the withdrawn amounts.

• After 6 months \(\frac{1}{4}\)th leaves.

o Remaining = \(\frac{3}{4}\)th.
• After another 3 months \(\frac{1}{3}\)th of \(\frac{3}{4}\)th left.

o This is \(\frac{1}{4}\)th of the total.
o Remaining = 1 – \(\frac{1}{4}\) – \(\frac{1}{4}\)= \(\frac{1}{2}\)
• From this I can see the answer is a multiple of 4.
• Let me take the number to be 4x.

o 6 months = 6 × \((4x)^2\)

= \(96x^2\)
o Next 3 months = 3× \((3x)^2\)

= \(27x^2\)
o End 3 months = 3 × (2x)^2.

= \(12x^2\)
• Total amount = 96\(x^2\) + 27\(x^2\) + 12\(x^2\) = 4860

Or, 135\(x^2\) = 4860
Or, \(x^2\) = 36
Or, x = 6
• Answer = 4x = 24