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# A man sold $400(Rs.20)$ shares of a company. Paying $5\%$ at $Rs.18$ and invested the proceeds in $(Rs.10)$ shares of another company paying $7\%$ at $Rs.12$ . How many $(Rs.10)$ shares did he buy and what was the change in his income?

Last updated date: 13th Jun 2024
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Hint: Nominal value $\left( {N.V} \right)$is the total value of all the shares, we get dividends on the nominal value of the shares which is called our income from the shares.
Useful formula:
Nominal value $\left( {N.V} \right)$ $=$ no. of shares $\times$ price of one share
Dividend $=$ rate $\times$ nominal value

Given data:
Total shares man have $= 400$
Price of one share $= Rs.20$
Dividend rate $= 5\%$
Sells the shares at $= Rs.18$
Bought the shares $(Rs.10)$ at $Rs.12$ a $7\%$ rate
Nominal value of $400$ shares
$= 400 \times 20 \\ = Rs.8000 \\$
Dividend from the shares at $5\%$
$= 5\% ofRs.8000 \\ = \dfrac{5}{{100}} \times 8000 \\ = Rs.400 \\$
He sells $400$ shares at $Rs.18$ so the nominal value will be
$= 400 \times 18 \\ = Rs.7200 \\$
Further, he buys $(Rs.10)$ shares at $Rs.12$
Total no. of share of $Rs.12$
$= \dfrac{{7200}}{{12}} \\ = 600 \\$
So 600 shares of $(Rs.10)$ did he buy
Dividend at $7\%$ will be
$= 7\% of600 \\ = \dfrac{7}{{100}} \times 600 \\ = Rs.420 \\$
Change in income will be
$= 420 - 400 \\ = Rs.20 \\$
Thus he bought a total $600(Rs.10)$ shares and the change in his income is Rs.20.

Note: Nominal value is also called face value of the shares at which shares are sold and bought and dividend is always calculated on face value of the shares.
Note: When the percentage sign is removed then the number is divided by $100$ . And according to $BODMAS$ rule, OF means multiply.