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प्रश्न
A man invests a certain sum of money in 6% hundred-rupee shares at Rs. 12 premium. When the shares fell to Rs. 96, he sold out all the shares bought and invested the proceed in 10%, ten-rupee shares at Rs. 8. If the change in his income is Rs. 540, find the sum invested originally.
उत्तर
Let the original sum invested = x
The number of Rs. 100 shares purchased at premium of Rs. 12
= `x/(100 + 12)`
= `x/112`
The income per original share at 6% = Rs. 6
Total Income = (Number of shares) × (Earning per share)
= (Number of shares) × 6
= `x/112 xx 6`
= `(3x)/56`
Proceeds from sale of original share at Rs. 96 per share
= (Number of shares) × 96
= `x/112 xx 96`
= `(6x)/7`
Number of Rs. 10 shares purchased at 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 Rs. 10 at 10%
= `10/100 xx 10`
= Rs. 1
Total income from new shares
= (Number of shares) × (Income per share)
= `(3x)/28 xx 1`
= `(3x)/28`
Given change in income = 540
Income from old shares – Income from new shares = 540
∴ `540 = (3x)/28 - (3x)/56 = (3x)/56`
∴ x = `540/(3/56)` = 10,080
Thus, the original sum invested is Rs. 10,080.
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