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Question
Payal had Rs 125 shares of 'Asian Chemicals' paying 12% dividend. She sold them at Rs 150 and invested the proceeds in Rs 50 shares of 'Saras Chemicals' at Rs 40 and paying 10% dividend. She thus increased her income by Rs 825. Find the number of shares of 'Asian chemicals' that Payal sold.
Solution
For shares of 'Asian Chemicals':
Let x be the no. of shares sold by Pay al.
Nominal value of each share =Rs 125
Face value of x shares = Rs 125x
Market value of each share = Rs 150
Market value of x shares = Rs 150x = proceeds from selling
Dividend = 12 % of Rs 125x = `12/100` x Rs 125 x = Rs 15 x .......... (i)
For shares of 'Saras Chemicals':
Market value of each share = Rs 40
Number of shares bought= proceeds from selling 'Asian Chemicals' /market value of 'Saras Chemicals'
=`(150 x)/40 = (15 x)/4`
Nominal value of each share =Rs 50
Face value of `(15 x)/4` shares = Rs `50 xx (15 x)/4` = Rs 187.5 x
Dividend = 10 % of Rs 187.5 x = Rs `(10 xx 187.5 x)/100` = Rs 18.75 x ......(ii)
Increase in annual income =Rs 825 =subtraction of (i) from (ii)
Rs (18.75x-15x) =Rs 825
⇒ 3.75x =Rs 825
⇒ x = 220
Therefore, Payal sold 220 shares
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