The simple interest on a certain sum for 8 months at 4% simple interest is Rs. 129 less than the simple interest on the same sum for 15 months at 5% per annum. Find the sum.

Let the sum be x.

According to the question :

$\frac{x \times 8 \times 4}{12 \times 100} = \frac{x \times 15 \times 5}{12 \times 100} - 129$

$\Rightarrow \frac{x \times 15 \times 5}{12 \times 100} - \frac{x \times 8 \times 4}{12 \times 100} = 129$

$\Rightarrow \frac{75x - 32x}{12 \times 100} = 129$

$\Rightarrow 43x = 129 \times 1200$

$\Rightarrow x = \mathrm{Rs}. 3600$

Hence, the correct answer is Rs. 3600.