The difference between the simple interest and the true

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The difference between the simple interest and the true discount on a certain sum for 6 months at 4% is Rs. 15. Find the sum ?

∵ 15 = [A x (4 x 1/2)²] / [100(100 + 4 x 1/2)]
⇒ 15 = (A x 4) / (100 x 102)
⇒ A = 15 x 25 x 102
∴ A = Rs. 38, 250.