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Shantanu has a choice to invest in Rs.10 shares of two firms at Rs.13 or at Rs.16. If the first firm pays a 5% dividend and the second firm pays a 6% dividend per annum - Mathematics and Statistics

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Sum

Shantanu has a choice to invest in Rs.10 shares of two firms at Rs.13 or at Rs.16. If the first firm pays a 5% dividend and the second firm pays a 6% dividend per annum,

find:

(i) Which firm is paying better?

(ii) If Shantanu invests equally in both the firms and the difference between the return from them is Rs. 30. Find how much, in all, does he invest.

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Solution

i. For firm 1:

Face value of the share (F.V.) = ₹ 10

The market value of the share (M.V.) = ₹ 13

Dividend = 5%

∴ Annual income from the share = `5/100 xx 10`

= ₹ 0.5

Profit percentage = `("Annual income")/("Market value") xx 100`

= `0.5/13 xx 100`

= `50/13`            ..............(i)

≈ 3.85%

For firm 2:

Face value of the share (F.V.) = ₹ 10

Market value of the share (M.V.) = ₹ 16

Dividend = 5%

∴ Annual income from the share = `6/100 xx 10`

= ₹ 0.6

Profit percentage = `("Annual income")/("Market value") xx 100`

= `0.6/16 xx 100`

= `60/16`    ................(ii)

= 3.75%

Since the profit percentage from firm 1 > the profit percentage from firm 2, the first firm is paying better.

(ii) Let ‘X’ be the amount of Shantanu invests in each of the firms.

Given that difference between the return from them is ₹ 30, we have

`(50/13)/100 xx "X" - (60/16)/100 xx "X" = 30`  .....[From (i) and (ii)]

∴ `"X"(50/13 - 60/16) = 30 xx 100`

∴ `"X"((50 xx 16 - 60 xx 13)/(13 xx 16)) = 3000`

∴ `"X"((800 - 780)/(13 xx 16)) = 3000`

∴ `"X" = (3000 xx 13 xx 16)/20`

∴ X = 31,200

In all, Shantanu invests 2X = 2 × 31,200

= ₹ 62,400 /-

Concept: Shares and Dividends
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