A man invests equal sum of money in two firms paying 8% shares(Rs 100) at a premium of Rs 25 and 6% shares (Rs 100) at a discount of Rs 25.He finds that if with his total investment he had bought equal number of shares of each company,his income would have been Rs 142 less.Find his total investment.

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Solution

$Let the man invests Rs x in each company . For company A : Investment = Rs x Nominal value of each share = Rs 100 Market value of each share = Rs 125 Number of shares bought = \frac{x}{125} Rate of dividend = 8 % Dividend on 1 share = 8 % of Rs 100 = Rs 8 Dividend on (\frac{x}{125}) shares = Rs [\frac{8 x}{125}] For company B : Investment = Rs x Nominal value of each share = Rs 100 Market value of each share = Rs 75 Number of shares bought = \frac{x}{75} Rate of dividend = 6 % Dividend on 1 share = 6 % of Rs 100 = Rs 6 Dividend on (\frac{x}{75}) shares = Rs [\frac{6 x}{75}] now, total income = [\frac{8 x}{125}] + [\frac{6 x}{75}] = \frac{8 x}{125} + \frac{10 x}{125} = Rs [\frac{18 x}{125}] Let n be the no . of shares bought of each company . Total investment = Rs 2 x Market value of 1 share of company A = Rs 125 Market value of 1 share of company B = Rs 75 Now, according to given situation, 125 n + 75 n = 2 x \Rightarrow n = \frac{x}{100} Now, dividend on 1 share of company A = Rs 8 dividend on (\frac{x}{100}) shares of company A = Rs (\frac{8 x}{100}) Now, dividend on 1 share of company B = Rs 6 dividend on (\frac{x}{100}) shares of company B = Rs (\frac{6 x}{100}) Now, total income = \frac{8 x}{100} + \frac{6 x}{100} = \frac{14 x}{100} Now, according to question, \frac{18 x}{125} - \frac{14 x}{100} = 142 \Rightarrow 0.144 x - 0.14 x = 142 \Rightarrow 0.004 x = 142 \Rightarrow x = 35500 So, total money invested = Rs 2 x = Rs [2 \times 35500] = Rs 71000$

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