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# 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. Find the value of the first instalment

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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.

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1. ## 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

=36001200

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=18039d

=18039×2

=18078

=2a=102

a=102​/2

a=51 value of first installment

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