Question

Divide Rs 40,608 into two parts such that if one part is invested in 8% Rs 100 shares at
8% discount and the other part is invested in 9% R s100 shares at 8% premium , the
annual incomes , from both the investment , are equal

Answer 1

First part = Rs. 19872

Second part =  Rs. 20,736

Step-by-step explanation:

Given:

Total investment = Rs. 40,608

Let first part = Rs. y

Second part = Rs. (40,608 − y)

For First 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 of shares purchased = $\frac{1}{92}$ shares

Dividend % = 8 %

Dividend on 1 share = 8 % of Rs. 100 = Rs. 8

Total dividend = $\frac{y}{92} \times Rs. 8 = Rs. \frac{2y}{23}$

Foe second part

Nominal value of 1 share= Rs. 100

Market value of share = Rs. 100 + 8 % of Rs. 100

                                     = Rs. 100 + Rs. 8

                                     = Rs. 108

No. of shares purchased = $\frac{40608-y}{108}$  shares

Dividend % = 9 %

Dividend on 1 share = 9 % of Rs. 100 = Rs. 9

Total dividend = $\frac{40608-y}{108}\times Rs. 9$

                        = $Rs.\frac{9(40608-y)}{108}$

Given that both dividend are equal

Thus $Rs. \frac{2y}{23} =Rs.\frac{9(40608-y)}{108}$

$2y \times 108 = 23(365472-9y)$

$216 y =23\times 365472 - 207 y$

$216 y + 207 y=23\times 365472$

$423 y = 23 \times 365472$

$y=\frac{23 \times 365472}{423}$

$y =23 \times 864$

y = Rs. 19,872

First part = Rs. 19872

Second part = Rs 40,608 - Rs. 19872 = Rs. 20,736

Answer 2

Answer:

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