Question 1: Calculate the money required to buy :

(i) 350, Rs. 20 shares at a premium of Rs. 7

(i) 275, Rs. 60 shares at a discount of Rs. 10

(iii) 50, Rs. 75 shares quoted at Rs. 71.50

$\text{(i) No. of shares to be bought = 350 }$

$\text{Rs. 20 shares at a premium of Rs. 7 means; nominal value of the share is Rs. 20} \\ \\ \text{and its market value } = 20 + 7 =\text{ Rs. } 27$

$\text{Therefore Money required to buy 1 share } = \text{ Rs. } 27$

$\text{Therefore Money required to buy 350 shares } = 350 \times 27 = \text{ Rs. } 9450$

$\text{(ii) Money required to buy 1 share} = 60-10 = \text{ Rs. } 50$

$\text{Therefore Money required to buy 275 shares} = 275 \times 50 =\text{ Rs. } 13750$

$\text{(iii) Quoted price of a share means its market value. }$

$\text{Therefore Money required to buy 1 share } = \text{ Rs. } 71.50$

$\text{Therefore Money required to buy 50 shares } = 50 \times 71.50 = \text{ Rs. } 3575$

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Question 2: Ravi invested Rs. 6250 in shares of a company paying 6% dividend per annum. If he bought Rs. 25 shares for Rs.31.25 each, find his income from the investment.

$\displaystyle \text{Since, the market value of each share } = \text{ Rs. } 31.25 \text{ and the sum invested is} \text{ Rs. } 6250$

$\displaystyle \text{Therefore No. of shares bought by Ravi }= \frac{6250}{31.25} = 200$

$\displaystyle \text{Income (dividend) on one share }= 6\% \text{ of N.V. } = \frac{6}{100} \times 25 = \text{ Rs. } 1.5$

$\displaystyle \text{Therefore, his total income } =200 \times 1.50 = \text{ Rs. } 300$

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Question 3: Manoj buys Rs. 100 shares at Rs. 20 premium in a company paying 15% dividend. Find: (i) the market value of 200 shares; (ii) his annual income; (iii) his percentage income.

$\displaystyle \text{(i) Market value of 1 share } = 100 + 20 = \text{ Rs. } 120$

$\displaystyle \text{Therefore Market value of 200 share } = 200 \times 120 = \text{ Rs. } 24000$

$\displaystyle \text{(ii) Annual income } = \text{ No. of shares } \times \text{ Rate of dividend } \times \frac{N.V.}{F.V.} \text{ of 1 share }$

$\displaystyle = 200 \times \frac{15}{100} \times 100 = \text{ Rs. } 3000$

$\displaystyle \text{(iii) 3000 is the income obtained on investing} \text{ Rs. } 24000$

$\displaystyle \text{Therefore Percentage income }= \frac{3000}{24000} \times 100 = 12.5\%$

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Question 4: Rs. 67200 are invested in Rs. 100 shares which are quoted at Rs. 120. Find the income if 12% dividend is declared on the shares. [ ICSE Board 1982]

$\displaystyle \text{Therefore Sum invested }= \text{ Rs. } 67200$

$\displaystyle \text{and M.V. of each share }= \text{ Rs. } 120$

$\displaystyle \text{Therefore No. of shares bought }= \frac{67200}{120} = 560$

$\displaystyle \text{Given : dividend (income) on 1 share }= 12\% \text{ of N.V. } = 12\% \text{ of } 100 = \text{ Rs. } 12$

$\displaystyle \text{Therefore Total income from the shares } = 560 \times 12 = \text{ Rs. } 6720$

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Question 5: Find the dividend due at the end of a year on 250 shares of Rs. 50 each, if the half-yearly dividend is 4% of the value of the share. [ ICSE Board 1983]

$\displaystyle \text{Since Half-yearly dividend on 1 share } = 4\% \text{ of Rs. } 50$

$\displaystyle \text{Therefore The yearly dividend on 1 share } = 8\% \text{ of }50 = \frac{8}{100} \times 50 = \text{ Rs. }4$

$\displaystyle \text{Therefore Total dividend due at the end of the year } = 250 \times 4 = \text{ Rs. }1000$

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Question 6: A man bought 500 shares, each of face value Rs. 10, of a certain business concern and during the first year, after purchase, receives Rs. 400 as dividend on his shares. Find the rate of dividend on the shares. [ ICSE Board 1985]

$\displaystyle \text{Since Face value of each share } = \text{Rs. }10$

$\displaystyle \text{and the number of shares bought } = 500$

$\displaystyle \text{Since Total sum invested in shares } = 500 \times 10 = \text{Rs. }5000$

$\displaystyle \text{Since total dividend in the first year } = \text{Rs. }400$

$\displaystyle \text{Rate of dividend } = \frac{\text{Dividend}}{\text{Sum Invested}} \times 100 = \frac{400}{5000} \times 100 = 8\%$

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Question 7: Mukul invests Rs. 9000 in a company paying a dividend of 6% per annum when a share of face value Rs. 100  stands at Rs. 150. What is his annual income? If he sells 50% of his shares when the price rises to Rs. 200, what is his gain in this transaction? [ ICSE Board 1991]

$\displaystyle \text{Since Mukul invests Rs. 9000 and M.V. of each share } = \text{Rs. }150$

$\displaystyle \text{No. of shares bought by Mukul } = \frac{9000}{150} = 60$

$\displaystyle \text{His annual income on 1 share } = 6\% \text{ of }100 = \frac{6}{100} \times 100 = \text{ Rs. } 6$

$\displaystyle \text{Therefore His total annual income } = 60 \times 6 = \text{Rs. }360$

$\displaystyle \text{50\% of shares } = 50\% \text{ of } 60 = 30$

$\displaystyle \text{Therefore Money received on selling these shares } = 30 \times 200 = \text{Rs. }6000$

$\displaystyle \text{Also, for Mukul, cost of these shares } = 30 \times 150 = \text{Rs. }4500$

$\displaystyle \text{Mukul's gain in this transaction } = 6000 - 4500 = \text{Rs. }1500$

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Question 8: A man wants to buy 62 shares available at Rs. 132 ( par value being Rs. 100)

(i) How much he will have to invest ?

(ii) If the dividend is 7.5%, what will be his annual income ?

(iii) If he wants to increase his annual income by Rs.150 how many extra shares should he buy? [ ICSE Board 2002]

$\displaystyle \text{(i) He will have to invest } = 62 \times 132 = \text{Rs. }8184$

$\displaystyle \text{(ii) Dividend on 1 share } = 7.5\% \text{ of } 100 = \text{Rs. }7.50$

$\displaystyle \text{Therefore his annual income } = 62 \times 7.50 = \text{Rs. }465$

$\displaystyle \text{(iii) Since The man wants to increase his income by } Rs. 150$ $\displaystyle \text{and the income on one share } = \text{Rs. }7.5$

$\displaystyle \text{Therefore the no of extra shares he must buy } = \frac{150}{7.50} = 20$

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Question 9: A company with 4000 shares of nominal value of Rs. 110 each declares an annual dividend of 15%. Calculate:

(i) The total amount of dividend paid by the company

(ii) The annual income of shah Rukh who holds 88 shares in the company’

(iii) If he received only 10% on his investment, find the price Shah Rukh paid for each share [ ICSE Board 2008]

$\displaystyle \text{(i) Given number of shares } = 4000$

$\displaystyle \text{Nominal Value of each share } = \text{Rs. }110 \text{ and, Dividend } = 15\%$

$\displaystyle \text{Total amount of dividend paid by the company } \\ \\ = \text{Dividend on one share} \times \text{Number of shares } = \frac{15}{100} \times 110 \times 4000 = \text{Rs. } 66000$

$\displaystyle \text{(ii) The annual income of Shah Rukh } \\ \\ = \text{Dividend on one share} \times \text{Number of shares} = \frac{15}{100} \times 110 \times 88 = \text{Rs. } 1452$

$\displaystyle \text{(iii) Let Shah Rukh pays } \text{ Rs. } x \text{ for each share }$

$\displaystyle \text{Therefore } 10\% \text{ of } x = 15\% \text{ of } 110$

$\displaystyle \Rightarrow \frac{10x}{100} = \frac{15 \times 110}{100} \Rightarrow x = 165$

$\displaystyle \text{Shah Rukh paid for each share} = 165$

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Question 10: A man buys a Rs. 40 share in a company, which pays 10% dividend. He buys the share at such a price that his profit is 16% on his investment. At what price did he buy the share ?

$\displaystyle \text{Dividend (profit) given by the company on 1 share } = 10\% \text{ of } 40 = \text{Rs. }4$

$\displaystyle \text{Suppose the man buys one share for } \text{Rs. } x$

$\displaystyle \text{Therefore his profit }= 16\% \text{ of } x = \frac{16x}{100}$

$\displaystyle \text{According to the statement, } \frac{16x}{100} = 4 \Rightarrow x = 25$

$\displaystyle \text{Therefore the man buys each share for } \text{Rs. } 25$

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Question 11: Ajay, owns 560 shares of a company. The face value of each share is Rs. 25. The company declares a dividend of 9%. Calculate :

(i) the dividend that Ajay will get.

(ii) the rate of interest on his investment, if Ajay had paid Rs. 30 for each share

$\displaystyle \text{(i) Dividend on each share } = 9\% \text{ of } 25 = \frac{9}{100} \times 25= 2.25$

$\displaystyle \text{Therefore dividend that Ajay will get } = 2.25 \times 560 = \text{Rs. } 1260$

$\displaystyle \text{(ii) Let rate of interest on his investment } = x\%$

$\displaystyle \text{Since, Ajay paid Rs.30 for each share, market value of each share } = \text{Rs. } 30$

$\displaystyle \text{We know : }$

$\displaystyle \text{Interest on M.V = Dividend on N.V }$

$\displaystyle \Rightarrow x\% \text{ of } 30 = 9\% \text{ of } 25$

$\displaystyle \Rightarrow \frac{x}{100} \times 30 = \frac{9}{100} \times 25$

$\displaystyle \Rightarrow x = 7.5$

$\displaystyle \text{Therefore the rate of interest } = 7.5\%$

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Question 12: How much should a man invest in Rs. 50 shares selling at Rs. 60 to obtain an annual income of Rs. 900, if the dividend declared is 15 per cent ?

$\displaystyle \text{Since dividend on 1 share } = 15\% \text{ of } 50 = \text{Rs. }7.50$

$\displaystyle \text{Therefore number of shares bought } = \frac{\text{Total dividend}}{\text{Dividend on 1 share}} = \frac{9000}{7.50} = 120$

$\displaystyle \text{Since, market value of each share }= \text{Rs. }60$

$\displaystyle \text{Therefore sum invested by the man }= 129 \times 60 = \text{Rs. }7200$

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Question 13: A dividend of 9% was declared on Rs. 100 share selling at a certain price. If the rate of return is 7.5%, calculate :

(i) the market value of the share;

(ii) the amount to be invested to obtain an annual dividend of Rs. 630.  [ ICSE Board 2000]

$\displaystyle \text{(i) Let M. V. of a share } = \text{Rs. }x$

$\displaystyle \text{Since, Rate of return } \times \text{ M.V. = Rate of dividend } \times \text{ N.V. }$

$\displaystyle \Rightarrow \frac{7.5}{100} \times x = \frac{9}{100} \times 100 \Rightarrow x = 120$

$\displaystyle \text{Therefore M.V. of a share } = \text{Rs. }120$

$\displaystyle \text{(ii) Since Annual income on 1 share } = 9\% \text{ of } 10 = \text{Rs. }9$

$\displaystyle \text{Annual income on 1 share } = \frac{\text{Total annual income}}{\text{Annual income on 1 share}} = \frac{630}{9} = 70$

$\displaystyle \text{and, the amount to be invested = No. of shares bought } \times \text{ M.V. of 1 share }= 70 \times 120 = \text{Rs. }8400$

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Question 14: Which is a better investment : 12% Rs. 100 shares at 120 or 8% Rs.100 shares at 90?

$\displaystyle \text{Since, Profit\% on M.V. = Dividend\% on N.V. }$

In first case :

$\displaystyle \text{Profit\%} \text{ on } 120 = 12\% \text{ on } 100$

$\displaystyle \Rightarrow \frac{P}{100} \times 120 = \frac{12}{100} \times 100 \Rightarrow \text{Profit } = 10\%$

In second case :

$\displaystyle \text{Profit\%} \text{ on } 90 = 8\% \text{ on } 100$

$\displaystyle \Rightarrow \frac{P}{100} \times 90 = \frac{8}{100} \times 100 \Rightarrow \text{Profit } = 8.9\%$

Since The investment giving greater profit%, will be better.

Therefore the first investment is better.

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Question 15: A man sells 60, Rs. 15 shares of a company paying 12 per cent dividend, at Rs. 21 each and invests the proceeds in Rs. 6 shares of another company at Rs. 9 each. Find his change in income, if the second company pays a dividend of 8 per cent.

$\displaystyle \text{No. of shares = 60, N.V. of 1 share = Rs. 15 and rate of dividend } = 12\%$

$\displaystyle \text{Therefore Income on 1 share } = \frac{12}{100} \times 15 = \text{Rs. }1.80$

$\displaystyle \text{Therefore Total income } = 60 \times 1.8 = \text{Rs. }108$

$\displaystyle \text{Now, he sells all the shares for Rs. 21 each }$

$\displaystyle \text{Money obtained by selling all the 60 shares } = 60 \times 21 = \text{Rs. }1260$

$\displaystyle \text{In the 2nd case : }$

$\displaystyle \text{Sum invested = Rs. 1260, N.V. of 1 share = \text{Rs. } 6; M.V. of 1 share = } \text{Rs. } 9$

$\displaystyle \text{and rate of dividend } =8\%$

$\displaystyle \text{Therefore No. of shares bought } = \frac{1260}{9} = 140$

$\displaystyle \text{and dividend on 1 share } = \frac{8}{100} \times 6 = \text{Rs. }0.48$

$\displaystyle \text{Total income } = 140 \times 0.48 = \text{Rs. }67.20$

$\displaystyle \text{Therefore Change in income } =108 - 67.20 = \text{Rs. }40.80$

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Question 16: Mr. Ram Gopal invested Rs. 8000 in 7% Rs. 100 shares at Rs. 80. After a year he sold these shares at Rs. 75 each and invested the proceeds (including his dividend) in 18%, Rs. 25 shares at Rs. 41. Find :

(i) his dividend for the first Year

(ii) his annual income in the second year

(iii) the percentage increase in his return on his original investment [ ICSE Board 2006]

$\displaystyle \text{Given : Investment } = \text{Rs. } 8000 , \text{ Dividend } \% = 7\%, \\ \\ \text{ N.V. } = \text{Rs. } 100 \text{ and M.V. } = \text{Rs. } 80$

$\displaystyle \text{(i) No. of shares } = \frac{\text{Investment}}{\text{M.V.of each share}} = \frac{8000}{80} = 100$

$\displaystyle \text{Therefore dividend on 1 share } = 7\% \text{ of } 100 = \text{Rs. } 7$

$\displaystyle \text{Therefore His dividend for the first year } = 7 \times 100 = \text{Rs. } 700$

$\displaystyle \text{(ii) Since, each share is sold for } \text{Rs. } 75$

$\displaystyle \text{Therefore The proceeds (including dividend) = } 100 \times 75 + 700= \text{Rs. } 8200$

$\displaystyle \text{Now the sum invested }= \text{Rs. } 8200$

$\displaystyle \text{N.V. of each share }= \text{Rs. } 25$

$\displaystyle \text{M.V. of each share }= \text{Rs. } 41$

$\displaystyle \text{and, dividend }= 18\%$

$\displaystyle \text{Therefore No. of shares bought }= \frac{8200}{41} = 200$

$\displaystyle \text{Dividend on 1 share }= \frac{18}{100} \times 25 = \text{Rs. } 4.50$

$\displaystyle \text{Therefore Annual dividend (income) in the second year }= 200 \times 4.5 = \text{Rs. } 900$

$\displaystyle \text{(iii) Since, increase in return }= 900 - 700 = \text{Rs. } 200$

$\displaystyle \text{Therefore Percentage increase in return (on the original investment) } \\ \\ = \frac{200}{8000} \times 100 = 2.5\%$

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Question 17: Ashok and Sandeep invest Rs. 18000 each in buying shares of two different companies. Ashok buys 7.5% Rs. 100 shares at a discount of 20% ,whereas Sandeep buys Rs. 50 shares at a premium of 20%. If both receive equal dividend at the end of the year, find the rate of dividend received by Sandeep

For Ashok

$\displaystyle \text{Sum invested } = \text{Rs. } 18000$

$\displaystyle \text{N.V. of each share } = \text{Rs. } 100$

$\displaystyle \text{M.V. of each share } = 100 - \frac{20}{100} \times 100 = \text{Rs. } 80$

$\displaystyle \text{Therefore Number of shares bought } = \frac{18000}{80} = 225$

$\displaystyle \text{Dividend on I share } =\frac{7.5}{100} \times 100 = \text{Rs. } 7.5$

$\displaystyle \text{Therefore Total dividend received } = 225 \times 7.50 = \text{Rs. } 1687.50$

For Sandeep

$\displaystyle \text{Sum invested } =\text{Rs. } 18000$

$\displaystyle \text{N.V. of each share } = \text{Rs. } 50$

$\displaystyle \text{M.V. of each share } = 50 + \frac{20}{100} \times 50 = \text{Rs. } 60$

$\displaystyle \text{Number of shares bought } = \frac{18000}{60} = 300$

Now, we have two methods of finding the rate of dividend.

It is given that Ashok and Sandeep receive equal dividend

Therefore Total dividend received by Sandeep = Total dividend received by Ashok $\displaystyle = \text{Rs. } 1687.50$

$\displaystyle \text{Dividend on 300 shares } = \text{Rs. } 1687.50$

$\displaystyle \text{And, dividend on each share } = \frac{1687.50}{300} = \text{Rs. } \frac{45}{8}$

$\displaystyle \text{Since, N.V. of each share } = \text{Rs. } 50$

$\displaystyle \text{On Rs. 50, dividend } =\text{Rs. } \frac{45}{8}$

$\displaystyle \text{Rate of dividend } = \frac{45}{8 \times 50} \times 100 = 11.25\%$

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Question 18: John had 1000 shares of a company with a face value of Rs. 40 and paying 8% dividend. He sold some of these shares at a discount of 10% and invested the proceeds in Rs. 20 shares at a premium of 50% and paying 12% dividend. If the change in his income is Rs.192, find the number of shares sold by John.

$\displaystyle \text{Let the number of shares sold by John be } x$

ln the first case :

$\displaystyle \text{Since N.V. of each share } = \text{Rs. } 40 \ \ \ \ \text{and rate of dividend } = 8\%$

$\displaystyle \text{Dividend on each share } = \frac{8}{100} \times 40 = \text{Rs. } 3.2$

$\displaystyle \text{and, dividend on } x \text{ shares } = \text{Rs. } 3.2x$

$\displaystyle \text{He sold each share for Rs. 40 - 10\% of Rs. 40 i.e for Rs. 36 }$

$\displaystyle \text{Therefore Money obtained by selling } x \text{ shares } = \text{Rs. } 36x$

In second case :

$\displaystyle \text{Sum invested } = \text{Rs. } 36x$

$\displaystyle \text{N.V. of each share } =\text{Rs. } 20$

$\displaystyle \text{M.V. of each share } = 20 + \frac{50}{100} \times 20 = \text{Rs. } 30$

$\displaystyle \text{Number of shares bought } = \frac{\text{sum invested}}{\text{M.V. of each share } } = \frac{36x}{30} = 1.2x$

$\displaystyle \text{Since, dividend on each share } = \frac{12}{100} \times 20 = \text{Rs. } 2.4$

$\displaystyle \text{Total dividend received } = 1.2x \times 2.4 = \text{Rs. } 2.88 x$

$\displaystyle \text{Given, change in income } = \text{Rs. } 192$

$\displaystyle 3.20x-2.88x = 192 \Rightarrow x = 600$

$\displaystyle \text{Number of shares sold by John } = 600$

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Question 19: Divide Rs. 40608 into two parts such that if one part is invested in 8% Rs. 100 shares at 8% discount and the other part is invested in 9% Rs. 100 shares at 8% premium, the annual incomes, from both the investment, are equal

$\displaystyle \text{Let the two parts be Rs. } x \text{ and Rs. } (40608 - x)$

For 1st part :

$\displaystyle \text{N.V. of each share }= \text{Rs. } 100$

$\displaystyle \text{M.V. of each share }= 100 - \frac{8}{100} \times 100 = \text{Rs. } 92$

$\displaystyle \text{Number of shares bought }= \frac{x}{92}$

$\displaystyle \text{Dividend on each share }= \frac{8}{100} \times 100 = \text{Rs. } 8$

$\displaystyle \text{Total dividend }= 8 \times \frac{x}{92} = \text{Rs. } \frac{2x}{23}$

For 2nd part:

$\displaystyle \text{Investment }= \text{Rs. } (40608 - x)$

$\displaystyle \text{N.V. of each share }= \text{Rs. } 100$

$\displaystyle \text{M.V. of each share }= 100 + \frac{8}{100} \times 100 = \text{Rs. } 108$

$\displaystyle \text{Number of shares bought }= \frac{40608 - x}{108}$

$\displaystyle \text{Dividend on each share }= \frac{9}{100} \times 100 = \text{Rs. } 9$

$\displaystyle \text{Total dividend }= 9 \times \frac{40608 - x}{108} = \frac{40608 - x}{12}$

Given, that dividends (incomes) from both the investments are equal

$\displaystyle \Rightarrow \frac{2x}{23} = \frac{40608 - x}{12}$

On solving, we get :

$\displaystyle x = \text{Rs. } 19872 \text{ and } 40608 - x = 40608 - 19872 = \text{Rs. } 20736$

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Question 20: A man has choice to invest in hundred-rupee shares of two companies A and B. Shares of company A are available at a premium of 20% and it pays 8% dividend whereas shares of company B are available at a discount of 10% and it pays 7% dividend. If the man invests equally in both the companies and the sum of the return from them is Rs. 936, find how much, in all, does he invest?

$\displaystyle \text{Let the man invests Rs. } x \text{ in each company }$

For company A :

$\displaystyle \text{N.V. of each share }= \text{Rs. } 100$

$\displaystyle \text{M.V. of each share }= 100 + \frac{20}{100} \times 100 = \text{Rs. } 120$

$\displaystyle \text{Number of shares bought }= \frac{x}{120}$

$\displaystyle \text{Dividend on each share }= \frac{8}{100} \times 100 = \text{Rs. } 8$

$\displaystyle \text{Total dividend }= 8 \times \frac{x}{120} = \text{Rs. } \frac{x}{15}$

For company B :

$\displaystyle \text{N.V. of each share }= \text{Rs. } 100$

$\displaystyle \text{M.V. of each share }= 100 - \frac{10}{100} \times 100 = \text{Rs. } 90$

$\displaystyle \text{Number of shares bought }= \frac{x}{90}$

$\displaystyle \text{Dividend on each share }= \frac{7}{100} \times 100 = \text{Rs. } 7$

$\displaystyle \text{Total dividend }= 7 \times \frac{ x}{90} = \frac{7 x}{90}$

$\displaystyle \text{Given, sum of dividend (return) from both the companies } = \text{Rs. } 936$

$\displaystyle \Rightarrow \frac{x}{15} + \frac{7x}{90} = 936$

$\displaystyle \Rightarrow x = 6480$

$\displaystyle \text{The man invests Rs. 6480 in each of the two companies.}$

$\displaystyle \text{Therefore the man invests in all }= 2 \times 6480 = \text{Rs. }12960$