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Question
Ananth had Rs 50 shares of 'Esco' paying 6% dividend. He sold them at a market price of Rs 80 and invested the proceeds in buying Rs 100 shares of 'Y2K Software' at Rs 150 and paying 11% dividend. He thus increased his annual income by Rs 2,150. How many shares of 'Esco' did he sell?
Solution
For shares of 'Esoo':
Let x be the no. of shares sold by Ananth.
Nominal value of each share =Rs 50
Face value of x shares =Rs 50x
Market value of each share = Rs 80
Market value of x shares = Rs 80x = proceeds from selling
Dividend = 6 % of Rs 50 x = `6/100` × Rs 50 x = Rs 3x ......(i)
For shares of 'Y2K Softvvare':
Market value of each share = Rs 150
Number of shares bought= proceeds from selling 'Esco' / market value of 'Y2K Softvvare'
`= (80 x)/150 = (8x)/15`
Nominal value of each share =Rs 100
Face value of `(8 x)/15` shares = Rs Rs 100 x `(8 x)/15` = Rs 53.33 x
Dividend = 11 % of Rs 53.33x = Rs `(11 xx 53.33 x)/100` = Rs 5.86 x ...........(ii)
Increase in annual income =Rs 2, 150 =subtraction of (i) from (ii)
Rs (5.86x - 3x) =Rs 2,150
2.86x =Rs 2,150
⇒ x = 751
Therefore, Ananth sold 751 shares
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