# A man deposites an amount to the bank. In which his amount doubles in one year. But, Bank cut off 65 rupees after doubling the amount in one year. After 6th year doubling and charging 65, the amount became zero. What is amount ????????

1
by AjiteshGaurav

2015-08-21T01:40:40+05:30

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Deposited amount = P
maturity amount = 2 P at the end of one year.
balance after Rs 65 taken out :  P1 = 2 P - 65

balance after year 2 :  P2 = 2 P1 - 65  = 2² P - 65 (2 + 1)
balance after year 3 :    P3 = 2 P2 - 65  = 2³ P - 65 * (4 + 2 + 1)

balance after n th year  =  Pn  = 2^n P - 65 * (2^{n-1} + 2^{n-2} + ... + 4 + 2 + 1)
= Pn = 2^n * P - 65 * (2^n - 1)            using G.P.
= 2^n * (P - 65) + 65
for n = 6,  Pn = 0
=>    64 * (P - 65) = - 65

=>  P = 65 - 65/64 = 65 * 63/64 = Rs 63.984375

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