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2015-09-21T14:09:22+05:30

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There is no mention of interest here.  Hence we just add the repayments.

Loan P = 6, 500
repayments =  610 + 580 + 550 + 520 + .....n terms
  common difference = 30 .    This is arithmetic progression.
   Nth term = 610 - (n-1) 30
sum  =  [610 + 610 - (n-1) 30] * N / 2  = 6, 500
               N [1, 220 - 30 (N-1)  ]  = 13, 000
               125 N  - 3 N² = 1, 300
                 3 N² - 125 N + 1,300
  N = [ 125 +-  √[ 125² - 15600] ] /6 =
     N = 20

In 20 months he is able to repay the loan.

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