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50 shares at 8%and the other part is invested in 8% 25 shares at 8% discount, then theDivide20304 into two parts such that if one part is invested in 900annual incomes from both the investments are equal |
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Answer» Let the two parts in which Rs.20304 is to be divided be Rs. x and Rs.(20304 - x). In First Case, Investment = Rs.x.Rate of Dividend = 9%.Nominal Value of 1 Share(N.V.) = Rs. 50Market Value of 1 Share(M.V.) = 50 + 50 × 8/100= 50 + 4= Rs. 52∵ Number of Shares = Sum Invested/M.V. of 1 Share∴ No. of Shares = x/54 ∵ Annual Income = No. of Shares× Rate of Dividend× N.V. of 1 Share.∴ Annual Income = x/54× 9/100× 50 ⇒ Annual Income = x/12 In Second Case, Investment = Rs. (20304 - x)N.V. of 1 Share = Rs. 25M.V. of 1 Share = 25 - 25× 8/100= 25 - 2= Rs. 23Rate of Dividend = 8 %No. of Shares = (20304- x)/23 Annual Income = (20304 - x)/23× 8/100× 25= Rs. 2(20304 - x)/23 According to the Question,Annual Income from both Investments are equals.∴ x/12 = 2(20304 - x)/23⇒ 23x = 24(20304) - 24x⇒ 24x + 23x = 24× 20304⇒ 47x = 487296⇒ x = Rs. 10368 Thus, First part is Rs. 10368. Second Part = 20304 - 10368= Rs. 9936 |
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