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.

Answer 1

Total investment = Rs. 50,760

Let 1^st part = Rs. y

2^nd part = Rs. (50,760 – y)

For 1^st 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 2^nd 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 × 108 = 23(456840 – 9y)

⇒ 216y = 456840 × 23 – 207y

⇒ 423y = 456840 × 23

⇒ `y = (456840 xx 23)/423`

⇒ y = Rs. 24,840

1^st part = Rs. 24,840

2^nd part = Rs. 50,760 – Rs. 24,840 = Rs. 25,920