Find the value of the first instalment, Mathematics

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A man arranges to pay a debt of Rs.3600 in 40 monthly instalments which are in a AP. When 30 instalments are paid he dies leaving one third of the debt unpaid. Find the value of the first instalment.

Ans: Let the value of I instalment be x S₄₀ = 3600.

⇒ 40/2 [2a + 39d ]=3600

⇒2a + 39d = 180 - 1

S₃₀ = 30/2 [2a + 29d ]=2400

⇒30a + 435d = 2400

⇒2a + 29d = 160 - 2

Solve 1 & 2 to get

d = 2 a = 51.

∴ I instalment = Rs.51.

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