Question 112653
The total amount invested = $12500 


Let x be the amount invested in the first part at the rate of 7% for a duration of 1 yr


Therefore Simple Interest(SI) = PTR/100     


where P = principle T = time and R = rate 


SI = x * 1 * (7/100)  -----------------------(1)


Let the remaining amount be (12,500 - x) invested at 6% for a duration of 1 yr 


SI = (12,500 - x) * 1 * (6/100) -------------------(2)


It is told that the interest earned by both the investments is the same.


so equating EQN'S (1) and (2) we get: 


{{{x * 7/100}}} = (12,500 - x){{{6/100}}} 


Solving for x we get:


7x = (12,500 - x)6 


==> 7x = 75,000 - 6x 


Adding 6x on both sides we get:


13x = 75,000 


==> {{{x = 75,000/13}}} 


==> x = 5769.230 was invested at 7% 


So, now the other value is got by:  



==> 12,500 - 5769.230 = 6730.769 was invested at 6% 


thus the solution.