Question

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Answer 1

Answer:

Principal (i) = 12000 Rs

After 1 year he paid back Rs 4000

Let the rate of interest be r Hence,

the principle after 1 year

= 12000(1+r/100)-4000

Now it is given that

C.I for 2nd year = 920

Hence,

{12000(1+r/100)-4000}(1+r/100)

= {12000(1+r/100)-4000 +920} => (1+r/100) = {12000(1+r/100)-4000 +920}/{12000(1+r/100)-4000}

=> (1+r/100) = {8920+120r}/{8000+120r}

=> r/100 = {8920+120r}/{8000+120r} - 1

=> r/100 = 920/8000+120r

=> 120r^2+8000r-92000 = 0 => 3r^2+200r-2300=0 => 3r^2 -30r+230r-2300=0

=> 3r(r-10) + 230(r-10)=0

=> (3r+230)(r-10)=0

Since rate cannot be negative Hence r = 10

Therefore rate of interest =10%

2. Now initial principle = 12000 C.I for 1st year

= 12000(1+10/100)-12000 = 13200-12000 = 1200

C.I. for 2nd year = 920

Hence sum of principle and interest of both years

=12000+1200+920

=14120

But he paid back 4000 Hence amount of debt at the end of 2nd year = 14120 - 4000 = 10120 Rs.