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The difference between the simple interest and true discount on a certain sum of money for 6 months at 12% per annum is Rs. 25. Find the sum.

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The difference between the simple interest and true discount on a certain sum of money for 6 months at 12% per annum is Rs. 25. Find the sum.

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Let the sum be Rs. x. Then, 

T.D. = (x*25/2*1/2)/(100+(25/2*1/2)) = x*25/4*4/425 = x/17 

S.I = x*25/2*1/2*1/100 = x/16 

x/16-x/17=25 

=>17x-16x=25*16*17 

=>x=6800 

Hence, sum due = Rs. 6800.

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