A man has some shares of Rs. 100 par value paying 6% dividend. He sells half of these at a discount of 10% and invests the proceeds in 7% Rs. 50 share at premium of Rs. 10. This transaction decreases his income from dividends by Rs. 120 . Calculate :
(i) the number of shares before the transaction.
(ii) the number of shares he sold.
(iii) his initial annual income from shares.

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Solution

Step 1:
Given information:
Value of one share $= Rs . 100$
Dividend $= 6 %$
Decrease in income from dividends $= Rs . 120$
Step 2:
Calculate the number of shares:
Let the number of shares be x.
Value of x shares $= x \times 100 = 100 x$
Since shares of Rs.100 par value paying 6% dividend.
$∴ Dividend = \frac{6}{100} \times 100 x \Rightarrow Dividend = Rs . 6 x$
Since the man sells half of the shares,
$∴ Dividend on half shares = \frac{6 x}{2} = Rs . 3 x$
and number of shares sold out $= \frac{x}{2}$
The amount received at a 10% discount is computed as;
$Amount = \frac{x}{2} \times 90 = Rs . 45 x$
In the investment of $Rs . 45 x$ , the number of shares purchased $= \frac{45}{60} x$
$∴ Amount of shares = \frac{45}{60} x \times 50 = Rs . \frac{225}{6} x$
So that, the income at the rate of 7% is computed as:
$Income = \frac{225}{6} x \times \frac{7}{100} Income = Rs . \frac{21}{8} x$
Difference of income $= 3 x - \frac{21}{8} x = \frac{3}{8} x$
Since this transaction decreases his income from dividends by $Rs . 120$ ,
$∴ \frac{3}{8} x = 120 \Rightarrow x = \frac{120 \times 8}{3} \Rightarrow x = 320$
Therefore, Number of shares $= 320$
And the number of shares he sold $= \frac{320}{2} = 160$
hence, Initial annual income $= 320 \times 6 = Rs . 1, 920$
Hence,
(i) The number of shares is $320$ .
(ii) He sold $160$ shares.
(iii) Initial annual income is $Rs . 1920$

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