a man arranges to pay a debt of rs3600 in 40

Question

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.