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Question
Divide Rs. 50,760 into two parts such that if one part is invested in 8% Rs. 100 shares at 8% discount and the other in 9% Rs. 100 shares at 8% premium, the annual incomes from both the investments are equal.
Solution
Total investment = Rs. 50,760
Let 1st part = Rs. y
2nd part = Rs. (50,760 – y)
For 1st part:
Nominal value of 1 share = Rs. 100
Market value of 1 share = Rs. 100 – 8% of Rs. 100
= Rs. 100 – Rs. 8
= Rs. 92
∴ No. shares purached = `y/92` shares
Dividend% = 8%
Dividend on 1 share = 8% of Rs. 100 = Rs. 8
Total dividend = `y/92 xx Rs. 8 = Rs. (2y)/23`
For 2nd part:
Nominal value of 1 share = Rs. 100
Market value of 1 share = Rs. 100 + 8% of Rs. 100
= Rs. 100 + Rs. 8
= Rs. 108
∴ No of shares purchased = `(50760 - y)/108` shares
Dividend% = 9%
Dividend on 1 share = 9% of Rs. 100 = Rs. 9
Total dividend = `(50760 - y)/108 xx Rs. 9`
= `Rs. (9(50760 - y))/108`
Given that both dividend are equal
Then `Rs. (2y)/23 = Rs. (9(50760 - y))/108`
`=> 2y xx 108 = 23(456840 - 9y)`
`=> 216y = 456840 xx 23 - 207y`
`=> 423y = 456840 xx 23`
`=> y= (456840 xx 23)/423 = Rs. 24,840`
1st part = Rs. 24,840
2nd part = Rs. 50,760 – Rs. 24,840 = Rs. 25,920
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