Question

a man borrowed a sum of money and agrees to pay off by paying Rs3150 at the end of first year and Rs 4410 at the end of second year .if the rate if C.I. is 5%p.a. ,find the sum...

Answer 1

First year:

Let sum be Rs. x
r = 5% p.a
n = 1 year

I = Prn/100 = x*5*1/100 = Rs. x/20
Amount = x+(x/20) = Rs. 21x/20

Second Year:

P = (21x/20)-3150 = Rs. (21x-6300)/20

I = (21x-6300)*5/(100*20) = Rs. (21x-6300)/400
Amount = (21x-6300)/20+(21x-6300)/400
= (420x-126000+21x-6300)/400
= Rs. (441x-132300)/400

If he pays Rs. 4410 now, he would clear off his debt.
∴ Amount = Rs. 4410

=> 4410 = (441x-132300)/400
=> 1764000 = 441x-132300
=> 441x = 1896300
=> x = Rs. 4300

Answer 2

Let The Principal = x
Rate Percent = 5%
Time = 2 years = 1+1
Interest = PRT/100
             = x * 5 * 1/100
             = x/20
Den he pays 3150 at the end of first year
So principal for second year = x + x/20 - 3150
                                              = 21x/20 - 3150
Interest for second year = (21x/20 - 3150) * 5*1 /100
                                       = (21x/20 - 3150) /20
So amount left after second year =  (21x/20 - 3150) + [(21x/20 - 3150) /20]

He clears the amount by paying 4410 at the end of the second year
So,
21x - 3150 * 20 + 21x - 3150 = 4410
--------------------    ---------------
             20                  400
420x - 3150*20*20 + 21x - 3150 = 4410
-------------------------------------------
                          400
441x - 1263150 = 4410*400
441x - 1263150 = 1764000
441x = 1764000+1263150
441x= 3027150
x = 6864.28
Sum Of Money = Rs 6864.28