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# 32. Divide Rs. 20304 into two parts such that if one part is invested in 9% Rs. 50 shares at 8% premium and the other part is invested in 8% Rs. 25 shares at 8% discount, then the annual incomes from both the investment are equal.

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an important question from the book -ML aggarwal( avichal publication)class 10th , chapter3, shares and dividends ……..

we are to asked to divide Rs. 20304 into two parts on  that given condition that
if one part is invested in 9% Rs. 50 shares at 8% premium and
the other part is invested in 8% Rs. 25 shares at 8% discount,
then the annual incomes from both the investment are equal.

please solve the question. Q no. 36, exercise 3, ML Publication, share and dividends

Share

1. Let the two parts in which Rs.20304 is to be divided be Rs. x and Rs.(20304 – x).

In First Case,

Investment = Rs.x.
Rate of Dividend = 9%.
Nominal Value of 1 Share(N.V.) = Rs. 50
Market Value of 1 Share(M.V.) = 50 + 50 × 8/100
= 50 + 4
= Rs. 52
∵ Number of Shares = Sum Invested/M.V. of 1 Share
∴ No. of Shares = x/54

∵ Annual Income = No. of Shares × Rate of Dividend × N.V. of 1 Share.
∴ Annual Income = x/54 × 9/100 × 50
⇒ Annual Income = x/12

In Second Case,

Investment = Rs. (20304 – x)
N.V. of 1 Share = Rs. 25
M.V. of 1 Share = 25 – 25 × 8/100
= 25 – 2
= Rs. 23
Rate of Dividend = 8 %
No. of Shares = (20304- x)/23

Annual Income = (20304 – x)/23 × 8/100 × 25
= Rs. 2(20304 – x)/23

According to the Question,
Annual Income from both Investments are equals.
∴ x/12 = 2(20304 – x)/23
⇒ 23x = 24(20304) – 24x
⇒ 24x + 23x = 24 × 20304
⇒ 47x = 487296
⇒ x = Rs. 10368

Thus, First part is Rs. 10368.

Second Part = 20304 – 10368
= Rs. 9936

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