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 50760
Let 1st part = Rs y
2nd part = Rs (50760 - 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" (2"y")/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` share
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 `(2"y")/23 = "Rs" (9(50760 - "y"))/108`
`=> 2"y" xx 108 = 23(456840 - 9"y")`
`=> 216"y" = 456840 xx 23 - 207"y"`
`=> 423"y" = 456840 xx 23`
`=> "y"= (456840 xx 23)/423 = "Rs" 24840`
1 st part = Rs 24840
2nd part = Rs 50760- Rs 24840 = Rs 25920
