Divide ₹20304 into two parts such that if one part is invested in 9% ₹50 shares at 8% premium and the other part is invested in 8% ₹25 shares at 8% discount, then the annual incomes from both the investment are equal.

Let the investment in 9% ₹50 shares be ₹x, then the investment in 8% ₹25 shares = ₹(20304 - x)

9% ₹50 shares are at 8% premium
∴ Market Value of one 9% ₹50 share = ₹50 + 8% of ₹50 = ₹54

8% ₹25 shares are at 8% discount
∴ Market Value of one 8% ₹25 share = ₹25 - 8% of ₹25 = ₹23

$\text{Income on 1 share of ₹54} = 9\% \text{ of ₹50} = ₹4.50 \\[0.5em] \text{Income on ₹x} = ₹\dfrac{4.5}{54}x = ₹\dfrac{x}{12} \\[0.5em] \text{Income on 1 share of ₹23} = 8\% \text{ of ₹25} = ₹2 \\[0.5em] \text{Income on ₹(20304 -x)} = ₹\dfrac{2}{23}(20304 - x) \\[0.5em]$

But the annual incomes from both the investments should be equal

$\therefore \dfrac{x}{12} = \dfrac{2}{23}(20304 - x) \\[0.5em] \Rightarrow 23x = 487296 - 24x \\[0.5em] \Rightarrow 47x = 487296 \\[0.5em] \Rightarrow x = \dfrac{487296}{47} \\[0.5em] \Rightarrow x = 10368 \\[0.5em] \therefore (20304 -x) = 20304 - 10368 = 9936$

∴ Investment in 9% ₹50 shares at ₹54 = ₹10368
and Investment in 8% ₹25 shares at ₹23 = ₹9936