divide rupees 1015 20 into two parts such that if one part is invested in 8% rupees 100 shares at 8% discount and the other in 9% rupees 50 shares at 8% premium the annual income are equal
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Answer:
Let Rs x be invested in 8% in Rs 100 share at 8% discount and (101520 - x) be invested in 9% Rs 50 share at 8% premium. When Rs(101520 - x) is invested in 9% Rs 50 share at 8% premium. Market value of share = 50 + 8% of 50 = 50 × 108 100 = 54. Number of shares bought = 101520 - x 54 Dividend of each share = 9% of 50 = 9 100 × 50 = Rs 9 2 Total dividend = 101520 - x 54 × 9 2 = 101520 - x 12 . When x is invested in 8% in Rs 100 share at 8% discount. Market value of the share = Rs 100 - 8% of Rs 100. = 100 × 92 100 = Rs 92 Number of shares bought = Rs x 92 Dividend on each share = 8% of 100 = 8 100 ×100 = Rs 8. Total dividend = 8 × x 92 = 2x 23 2x 23 = 101520 - x 12 24x = 23 × 101520 - 23x (24+23)x = 23 × 101520 x = 23 × 101520 47 x = Rs 49680. ∴ 101520 - x = 51840. ∴ 51840 invested in 8% in 100 is share at 8% discount.
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