Divide ₹50,760 into two parts such that if one part is invested in 8% ₹ 100 shares at 8% discount and the other in 9% ₹ 100 shares at 8% premium, the annual incomes from both the investments are equal.

Let money invested be ₹ x and ₹ (50760 - x)

In first case :

M.V. = ₹ 100 - $\dfrac{8}{100}$ x 100 = ₹ 100 - ₹ 8 = ₹ 92.

No. of shares = $\dfrac{x}{92}$

Annual income = No. of shares × Rate of div. × N.V. of 1 share

= $\dfrac{x}{92} \times \dfrac{8}{100} \times 100 = \dfrac{2x}{23}$

In second case :

M.V. = ₹ 100 + $\dfrac{8}{100}$ x 100 = ₹ 100 + ₹ 8 = ₹ 108.

No. of shares = $\dfrac{50760 - x}{108}$

Annual income = No. of shares × Rate of div. × N.V. of 1 share

= $\dfrac{50760 - x}{108} \times \dfrac{9}{100} \times 100 = \dfrac{50760 - x}{12}$

Given, annual income are same,

$\therefore \dfrac{2x}{23} = \dfrac{50760 - x}{12} \\[1em] \Rightarrow 24x = 23(50760 - x) \\[1em] \Rightarrow 24x = 1167480 - 23x \\[1em] \Rightarrow 47x = 1167480 \\[1em] \Rightarrow x = \dfrac{1167480}{47} \\[1em] \Rightarrow x = 24,840$

50760 - x = ₹ 50760 - ₹ 24840 = ₹ 25,920.

Hence, money invested in first firm = ₹ 24,840 and in second firm = ₹ 25,920.