Question

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 at 8% discount, then the annual incomes of both the investment are equal.

Answer 1

Hello Dear.

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



Hope it helps.

Answer 2

Step-by-step explanation:

we will first divide divide the term into two parts i.e. x and 20304 -x

for the first half that is x :

rod=9%

sum invested=x

NV=50

premium=8%

for the second half that is 20304-x :

sum invested=20304-x

ROD=8%

NV=25

discount=8%.

some how due to crop I missed it from the pic