An important question from arithmetic progression chapter in which we have to find the value of the first instalment if a man arranges to pay off a debt of Rs.3600 in 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid he dies leaving one-third of the debt unpaid.
Book – RS Aggarwal, Class 10, chapter 5C, question no 47.
Debt of Rs.3600 is to be paid on 40 annual installments.
∴S40=3600........(i)
After 30 installments 31 of the debt is unpaid
∴S30=3600− 1/3of 3600
=3600−1200
S30=2400
in (i) we get.
S40=40/2[2a+39d]=360
⇒2a+39d=180……(iii)
in (ii)
S30=2400
⇒30/2[2a+29d]=2400
⇒2a+29d=2400……(iv)
(iii)−(iv)
10d−=20
⇒d=2
∴2a=180−39d
=180−39×2
=180−78
=2a=102
⇒a=102/2
⇒a=51 value of first installment