Total amount of debt to be oaid in 40 installments = Rs 3600
After 30 installments, one-third of his debt is unpaid. This means that two-third of his payment is done.
Therefore, the amount he paid in 30 installments = 2/3(3600) = 2(1200) = 2400
Let a be the first installment and d be the common difference between them.
We know from the formula of AP that,
Sn = n/2[2a+(n-1)d]
Substituting the values of a and d,
S30 = 30/2[2a+(30-1)d]
Similarly, a and d are calculated for 40 installments
S40 = 40/2[2a+(40-1)d]
Subtracting eq.1 and eq.2
a-a = (180-39d/2)-(160-29d/2)
Substituting the value of d,
Therefore, Rs.51 was paid in the first installment.