Let the time of the recurring deposit in month be n 

Monthly installment = ₹1600

Amount Deposited = 1600 x n = 1600n 

Rate of Interest = 9%

Interest = P $\times$ $\frac{n\times (n+1)}{2\times 12}$ $\times$  $\frac{r}{100}$

             =  1600 $\times$ $\frac{n\times (n+1)}{2\times 12}$ $\times$ $\frac{9}{100}$

             = 6 $\times$n $\times$ (n+1)

            = 6 $n^2$ + 6 n

Given Maturity Value = 65592

Maturity Value = Amount Deposited + Interest

     65592 = 1600n + 6 $n^2$ + 6 n

    65592 = 1606n + 6 $n^2$

   6 $n^2$ + 1606 n - 65592 = 0

   (n-36)(3n+911) = 0

n = 36 and n = -911/3 (neglecting -911/3 as n cannot be negative as it time period)

Therefore, the time for which he held the account = 36 months or 3 years.