#### 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 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" (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` 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 `(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" 24840`

1 st part = Rs 24840

2nd part = Rs 50760- Rs 24840 = Rs 25920