A man arranges to pay off a debt of RS. 3600 by 40 annual installments which form an A.P. When 30 of the installments are paid, he dies leaving one - third of thhe debt unpaid, find the value of the first installment.
Answers
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Answer:
The value of the first installment is 51.
Step-by-step explanation:
Given :
Total amount of Debt , S40 = 3600
Number of annual installments, n = 40
He paid 30 installment and he dies leaving 1/3 of the debt unpaid.
Unpaid amount = ⅓ × 3600 = 1200
Total payment he paid in 30 installment , S30 = 3600 - 1200 = 2400
S30 = 2400
By using the formula ,Sum of nth terms , Sn = n/2 [2a + (n – 1) d]
For 30 installments :
S30 = 30/2 [2a + (30 - 1)d]
2400 = 15 [2a + 29d]
2400/15 = [2a + 29d]
160 = 2a + 29d
2a = 160 - 29d
2a + 29d = 160 ……..(1)
For 40 installments :
S40 = 40/2 [2a + (n - 1) d]
3600 = 20 [2a + (40 -1) d]
3600/20 = 2a + 39d
180 = 2a + 39d
2a + 39d = 180 ………..(2)
On subtracting eq (i) from (ii),
2a + 39d = 180
2a + 29d = 160
(-) (-) (-)
----------------------
10d = 20
d = 20/10
d = 2
On Putting the value of d = 2 in eq (1),
2a + 29d = 160
2a + 29 (2) = 160
2a + 58 = 160
2a = 160 - 58
2a = 102
a = 102/2
a = 51
Hence, the value of the first installment is 51.
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