A borrows Rs. 8000 at 12 % per annum simple interest and B borrows Rs. 9100 at 10 % per annum simple interest. The years after which their amounts will be equal are ____ years.

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A borrows Rs. 8000 at 12 % per annum simple interest and B borrows Rs. 9100 at 10 % per annum simple interest. The years after which their amounts will be equal are 22 years.Given A borrows Rs. 8000 at 12 % per annum simple interest and B borrows Rs. 9100 at 10 % per annum simple interest.We know that,

S.I=
    
     P×R×T
    
     100

.Let the number of years = x.The S.I of A is

S.
    I
    1

, and the principle of A is

P
    1

. The amount is,

A
      1
     
     =S.
      I
      1
     
     +
      P
      1

=

P
        1
       
       ×
        r
        1
       
       ×T
      
       100
     
     +
      P
      1

=
      
       8000×12×T
      
       100
     
     +8000

=960T+8000

Also, amount = sum + S.I.The S.I of B is

S.
    I
    2

, and the principle of B is

P
    2

.

A
      2
     
     =S.
      I
      2
     
     +
      P
      2

=

P
        2
       
       ×
        r
        2
       
       ×T
      
       100
     
     +
      P
      2

=
      
       9100×10×T
      
       100
     
     +9100

=910T+9100

Now, equating both the amounts,

960T+8000=910T+9100

960T−910T=9100−8000

50T=1100

T=22 years

Therefore, time is 22 years.

A borrows Rs. 8000 at 12 % per annum simple interest and B borrows Rs. 9100 at 10 % per annum simple interest. The years after which their amounts will be equal are ____ years.

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