Shares and Dividend...Manish invested a certain sum in 6% 100 Rs shares at Rs 12 premium. When the shares fell to Rs 96, he sold out the shares and invested the proceeds in 10% 10 Rs shares at Rs...
Shares and Dividend...
Manish invested a certain sum in 6% 100 Rs shares at Rs 12 premium. When the shares fell to Rs 96, he sold out the shares and invested the proceeds in 10% 10 Rs shares at Rs 8. If the change in his income is Rs 540, find the sum invested.
Let the amount Manish invested in 6% income share at 12 premium be x . So the number of shares he invested = x/112.
The face value of this = 100x/112 and income on this face value at 6% is 100x/112*6% = 6x/112....................(1)
The selling of shares at 96 brings him an amount (x/112)96 = 96x/112. The number of shares of face value at 8 he could purchse from the amount 96x/112 is (6x/112)/8 = 12x/112 and the face value of these shares = (12x/112)10 =120x/112. The return at 10% for the face value of (120x/112 is (120x/112)10% =12x/112.................(2)
So the diffrence of income , from (1) and (2) is 12x/112-6x/112. But this is said to be equal to Rs540. Therefore, the required equation is:
12x/112 - 6x/112 = Rs 540 Or
(12-6)x = Rs540. Or
x = Rs 540*112/6 = Rs 10080
Original sum invested = x
Then number of Rs. 100 shares purchased at premium of Rs 12 = x/(100 +12) = x/112
The Income per original share @ 6%= Rs 6
Total Income = (Number of shares)*(earning per share)
= (Number of shares)*6 = (x/112)*6 = 3x/56
Proceeds from sale of original shares @ Rs. 96 per share
= (Number of Shares)*96 = (x/112)*96 = 6x/7
Number of Rs 10 shares purchased @ Rs 8 per share from proceeds of original shares
= (Proceeds from sale of original shares)/8 = (6x/7)/8 = 3x/28
Income per new share of Rs 10 @ 10% = (10/100)*10 = Rs.1
Total income from new shares
= (Number of shares)*(Income per share)
= (3x/28)*1 = 3x/28
Given change in income = 540 =
= (Income from old shares) - (Income from new shares)
540 = 3x/28 - 3x/56 = 3x/56
x = 540/(3/56) = 10080
Original sum invested = Rs.10,080