Divide ₹101520 into two parts such that if one part is invested in 8% ₹100 shares at 8% discount and the other in 9% ₹50 shares at 8% premium, the annual incomes are equal.

Let the investment in 8% ₹100 shares be ₹x, then the investment in 9% ₹50 shares = ₹(101520 - x)

8% ₹100 shares are at 8% discount
∴ Market Value of one 8% ₹100 share = ₹100 - 8% of ₹100 = ₹92

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

$\text{Income on 1 share of ₹92} = 8\% \text{ of ₹100} = ₹8 \\[0.5em] \text{Income on ₹x} = ₹\dfrac{8}{92}x == ₹\dfrac{2}{23}x \\[0.5em] \text{Income on 1 share of ₹54} = 9\% \text{ of ₹50} = ₹4.50 \\[0.5em] \text{Income on ₹(101520 - x)} = ₹\dfrac{4.5}{54}(101520 - x) = ₹\dfrac{101520 - x}{12} \\[0.5em]$

But the annual incomes from both the investments should be equal

$\therefore \dfrac{2x}{23} = \dfrac{101520 - x}{12} \\[0.5em] \Rightarrow 24x = 2334960 - 23x \\[0.5em] \Rightarrow 47x = 2334960 \\[0.5em] \Rightarrow x = \dfrac{2334960}{47} \\[0.5em] \Rightarrow x = 49680 \\[0.5em] \therefore (101520 -x) = 101520 - 49680 = 51840$

∴ Investment in 8% ₹100 shares at ₹92 = ₹49680
and Investment in 9% ₹50 shares at ₹54 = ₹51840