Question

A man invested ₹ 2000 in 3% stock at 80 and ₹ 3000 in 7% stock at 120. If the total sum invested in `5 1/4%` stock yields the same income, find the market price of one share of the last stock.

Answer 1

Given:

₹ 2000 invested in 3% stock at ₹ 80

₹ 3000 invested in 7% stock at ₹ 120

A total of ₹ 5000 invested in `5 1/4%` stock = 5.25% stock gives the same income

Income from 3% stock at ₹ 80

Nominal value `= 2000/80xx100`

= ₹ 2500

Income = 3% of 2500

`=3/100xx2500`

= ₹ 75

Income from 7% stock at ₹ 120

Nominal value = `3000/120xx100`

= ₹ 2500

Income = 7% of 2500

`=7/100xx2500`

= ₹ 175

Total income = ₹ 75 + ₹ 175 

= ₹ 250

This same income is received from ₹ 5000 invested in 5.25% stock

Let the market price of this stock = ₹ x

Nominal value `=5000/x xx100`

Income = 5.25% of nominal value

`= 5.25/100xx5000/x xx100`

`=(5.25xx5000)/x`

`= 26250/x = 250`

`=>x = 26250/250`

= ₹ 105