A person invested 20%, 30% and 25% of his savings in buying shares at par values of three different companies A, B and C which declare dividends of 10%, 12% and 15% respectively. If his total income on account of dividends be ₹4675, find his savings and the amount which he invested in buying shares of each company.

Let the savings of the person be ₹x.

Amount invested in company A

$= \dfrac{20}{100}x \\[0.5em] = \dfrac{x}{5}$

Amount invested in company B

$= \dfrac{30}{100}x \\[0.5em] = \dfrac{3x}{10}$

Amount invested in company C

$= \dfrac{25}{100}x \\[0.5em] = \dfrac{x}{4}$

As shares are at par so Nominal Value and Market Value of shares are equal.

Dividend from company A

$= \dfrac{10}{100} \times \dfrac{x}{5} \\[0.5em] = \dfrac{x}{50}$

Dividend from company B

$= \dfrac{12}{100} \times \dfrac{3x}{10} \\[0.5em] = \dfrac{9x}{250}$

Dividend from company C

$= \dfrac{15}{100} \times \dfrac{x}{4} \\[0.5em] = \dfrac{3x}{80}$

As per the given,

$\dfrac{x}{50} + \dfrac{9x}{250} + \dfrac{3x}{80} = 4675 \\[0.5em] \Rightarrow \dfrac{40x + 72x + 75x}{2000} = 4675 \\[0.5em] \Rightarrow \dfrac{187x}{2000} = 4675 \\[0.5em] \Rightarrow x = \dfrac{2000 \times 4675}{187}\\[0.5em] \Rightarrow x = 50000 \\[1.5em] \text{Savings of the person} = \bold{₹50000} \\[0.5em] \text{Investment in company A shares} = \dfrac{x}{5} = \dfrac{50000}{5} = \bold{₹10000} \\[0.5em] \text{Investment in company B shares} = \dfrac{3x}{10} = \dfrac{3 \times 50000}{10} = \bold{₹15000} \\[0.5em] \text{Investment in company C shares} = \dfrac{x}{4} = \dfrac{50000}{4} = \bold{₹12500} \\[0.5em]$