A man sells $100$ , $₹ 25$ shares of a company paying $10 %$ dividend, at $₹ 50$ each and invests the proceeds in $₹ 5$ shares of another company at $₹ 10$ each. Find his change in income, if the second company pays a dividend of $6 %$ .

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Solution

Step 1: Given Data:
Number of shares that the man sells, $N_{1} = 100$
Face value of 1^st company, $F_{1} = ₹ 25$
Dividend of 1^st company, $D_{1} = 10 %$
Market value of 1^st company, $M_{1} = ₹ 50$
Face value of 2^nd company, $F_{2} = ₹ 5$
Dividend of 2^nd company, $D_{2} = 6 %$
Market value of 2^nd company, $M_{2} = ₹ 10$
Step 2: Calculate the sale proceeds of man, after selling 100 shares at $M_{1}$ :
$S a l e p r o c e e d s = N u m b e r o f s h a r e s \times M a r k e t v a l u e$
$= N_{1} \times M_{1} = 100 \times 50 = ₹ 5000$
Step 3: Calculate the number of shares bought at $M_{2}$ :
$N u m b e r o f s h a r e s = \frac{I n v e s t m e n t}{M a r k e t v a l u e}$
$N_{2} = \frac{S e l l i n g P r i c e}{M_{2}} = \frac{5000}{10} = 500 shares$
Step 4: Calculate the annual income on 1^st and 2^nd company's shares, respectively:
$A n n u a l i n c o m e = N u m b e r o f s h a r e s \times F a c e v a l u e \times \frac{R a t e o f d i v i d e n d}{100}$
$A_{1} = N_{1} \times F_{1} \times \frac{D_{1}}{100} = 100 \times 25 \times \frac{10}{100} = ₹ 250$
$A_{2} = N_{2} \times F_{2} \times \frac{D_{2}}{100} = 500 \times 5 \times \frac{6}{100} = ₹ 150$
Step 5: Calculate the difference between the annual incomes of both the companies:
$D i f f e r e n c e i n a n n u a l i n c o m e s = A_{1} - A_{2}$
$= 250 - 150 = ₹ 100$
Final Answer: The change in the man's income is $₹ 100$ .

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