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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?

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Last updated date: 13th Jun 2024
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Answer
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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

Complete step-by-step answer:
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.