A man invests a certain sum of money in 6% hundred-rupee shares at ₹ 12 premium. When the shares fell to ₹ 96, he sold out all the shares bought and invested the proceed in 10%, ten-rupee shares at ₹ 8. If the change in his income is ₹ 540, find the sum invested originally.

Let sum originally invested be ₹ x,

M.V. of first type of shares = ₹ 100 + ₹ 12 = ₹ 112.

No. of shares = $\dfrac{x}{112}$

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

$= \dfrac{x}{112} \times \dfrac{6}{100} \times 100 \\[1em] = \dfrac{3x}{56}.$

S.P. of shares = ₹ 96 × $\dfrac{x}{112} = \dfrac{96x}{112}$

M.V. of second type of shares = ₹ 8

No. of second type of shares = $\dfrac{\dfrac{96x}{112}}{8} = \dfrac{12x}{112}$

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

$= \dfrac{12x}{112} \times \dfrac{10}{100} \times 10 \\[1em] = \dfrac{6x}{56}.$

Given, change in income = ₹ 540

$\therefore \dfrac{6x}{56} - \dfrac{3x}{56} = 540 \\[1em] \Rightarrow \dfrac{3x}{56} = 540 \\[1em] \Rightarrow x = \dfrac{540 \times 56}{3} = 10,080.$

Hence, sum invested originally = ₹ 10,080.