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 A man arrangesto pay off a debt of Rs. 3600 by 40 annual instalments which form an airthemtic series. When 30 of the instalments are paid, he diesleaving one-third of the debit unpaid, find the value of the first instalment.

Please help me to solve this problem.

Hi Priyanka!
 
The installment paid by the man in sequent months form an A.P. Let a be installment paid in the first month and d be the increase in the installment paid in the consecutive months.
 
Sn = (n/2) × [2a + (n – 1)d]
 
The debt paid in 30 months is 2/3 of Rs 3600 = Rs 2400
∴ S30 = 2400.
⇒ (30/2) × [2a + (30 – 1)d] = 2400
⇒ 15 × [2a + 29d] = 2400
⇒ 2a + 29d = 160  … (1)
 
The total sum is 3600 and the man paid it in 40 months.
∴ S40 = 3600.
⇒ (40/2) × [2a + (40 – 1)d] = 3600
⇒ 20 × [2a + 39d] = 3600
⇒ 2a + 39d = 180  … (2)
 
Subtracting both sides of equation (1) from equation (2);
10d = 20 
∴ d = 2
 
Substituting the value of d in equation (1);
2a + 29 × 2 = 160
⇒ 2a = 160 – 58 = 102
⇒ a = 51
 
Thus, the man paid Rs 51 in the first installment.
 
Hope! This will help you.
Cheers!

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thumbs up plz.

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thank u very much.

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I would like to tell u that u have done a little bit mistake in last that we have to find first installment so we have to take n = 40  so it is

Sn =  n/2[2a + (n-1)d]

3600 = 40/2 [ 2a + (40-1) 2 ]

3600 =  20 [2a + 39*2]

180 = 2a +78

180-78 = 2a

102 = 2a

a =51

as I know the answer of this question but I was not able to find d and for that you have helped me a lot so thank u very much.

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the total sum is 3600, thus Sn=3600.

let first installemnt be a and the difference be d.

the debt he paid = 2/3 * 3600 = 2400.                  (1/3 is unpaid)

installements = 30, thus, n = 30.

by using formula for Sn we get

Sn = 15[a + 29d]

2400/15 = a + 29d

a + 29d = 160            -----------------1

now, if he would have paid the total amount, then

3600 = 20[a + 39d]

a + 39d = 180      --------------------2

subtracting 1 from 2. we get

10d = 20 

thus, d = 2.

now, a + 29*2=160                (putting in 1)

so, a =160 - 58 = 102.

so the first installment = Rs. 102.

hope this helps.

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Thank u sir.

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