Question

Mr Joseph sold some Rs 100 shares paying 10% dividend at a discount of 25% and invested the proceeds in Rs 100 shares paying 16% dividend at a discount of 20%. By doing so, his income was increased by Rs 4,800. Find the number of shares originally held by Mr Joseph.

Answer 1

Let the number of shares be x

Annual income = Rate of dividend x Nominal value x Number of shares

`= 10/100 xx 100 xx x`

= 10x ....(i)

Since each share is sold at a discount of Rs 25%

Selling price of one share = `Rs 100 - 25/100 = Rs 75`

So the selling price of x shares = Rs 75x

The proceeds = the new investment = Rs 75x

Here the N.V = Rs 100

M.V of each share = Rs 80

Rate of dividend = 16%

Number of shares = `75x/80`

Annual income = Rate of dividend x Nominal value x Number of shares

`= 16/100 xx 100 xx (75x)/80`

= 15x .....(ii)

From i and ii we get

15x - 10x = 4800

`=> 5x = 4800`

`=> x = 960`

So the number of shares originally were 960