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Question

Gagan invested 80% of his savings in 10% Rs 100 shares at 20% premium and the rest of his savings in 20% Rs 50 shares at 20% discount. If his incomes from these shares is Rs 5,600, calculate :

(i) his investment in shares on the whole.

(ii) the number of shares of first kind that he bought.

(iii) percentage return, on the shares bought, on the whole.

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Solution

(i) Let the total savings be Rs.x,
For 1st part:
Nominal Value of each share = Rs. 100
Market Value of each share = 100+20 over 100(100) =Rs 120
Number of shares bought = fraction numerator 0.8 x over denominator 120 end fraction ...(lnvestment Rs x)
Dividend on each share = 10% of 100 = Rs 10 ...(Rate = 10%)
Total dividend = 10 cross times fraction numerator 0.8 x over denominator 120 end fraction equals R s. fraction numerator 0.8 x over denominator 12 end fraction

For 2nd part:
Nominal Value of each share = Rs.50
Market Value of each share = 50 - 20 over 100 left parenthesis 50 right parenthesis = Rs. 40
Number of shares bought = fraction numerator 0.2 x over denominator 40 end fraction ...(investment = Rs.x)
Dividend on each share = 20% of 50 = Rs. 10 ...(Rate = 20%)

Total dividend =10 cross times fraction numerator 0.2 x over denominator 40 end fraction space equals space fraction numerator 0.2 x over denominator 4 end fraction

Given that dividends (incomes) from both the investments are is Rs. 5600.
rightwards double arrow fraction numerator 0.8 x over denominator 12 end fraction plus fraction numerator 0.2 x over denominator 4 end fraction equals 5600 rightwards double arrow fraction numerator 0.8 x space plus space 0.6 x over denominator 4 end fraction equals 5600 rightwards double arrow x equals space fraction numerator 5600 space cross times space 12 over denominator 1.4 end fraction rightwards double arrow x equals space 48 comma 000
Thus, his investment in shares, on the whole, is Rs.48,000.

(ii) So, the number of shares bought =fraction numerator begin display style 0.8 x end style over denominator begin display style 120 end style end fraction equals fraction numerator begin display style 0.8 cross times 48 comma 000 end style over denominator begin display style 120 end style end fraction space equals space R s. space 320

(iii) total dividend (return) = fraction numerator begin display style 0.8 x end style over denominator begin display style 12 end style end fraction plus fraction numerator begin display style 0.2 x end style over denominator begin display style 4 end style end fraction equals fraction numerator begin display style 0.8 cross times left parenthesis 48 comma 000 right parenthesis end style over denominator begin display style 12 end style end fraction plus fraction numerator begin display style 0.2 cross times left parenthesis 48 comma 000 right parenthesis end style over denominator begin display style 4 end style end fraction equals space R s. space 5600

Percentage return = fraction numerator 5600 over denominator 48 comma 000 end fraction cross times 100 space equals space 11.667 percent sign


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