Divide 35400 into two parts such that if one part is invested in 9% rupees 100 shares at 4% discount and other in 12% former rupees 50 shares at 8% premium annual income from both the investment are equal
Answers
Answer:
Step-by-step explanation:
Let the two parts in which Rs.35400 is to be divided be Rs. x and Rs.(35400 - x).
In First Case,
Investment = Rs.x.
Rate of Dividend = 9%.
Nominal Value of 1 Share(N.V.) = Rs. 100
Market Value of 1 Share(M.V.) = 100 - 100 × 4/100
= Rs. 96
∵ Number of Shares = Sum Invested/M.V. of 1 Share
∴ No. of Shares = x/96
∵ Annual Income = No. of Shares × Rate of Dividend × N.V. of 1 Share.
∴ Annual Income = x/96 × 9/100 × 100
⇒ Annual Income = 9x/96
In Second Case,
Investment = Rs. (35400 - x)
N.V. of 1 Share = Rs. 50
M.V. of 1 Share = 50 + 50 × 8/100
= Rs. 54
Rate of Dividend = 12 %
No. of Shares = (35400 - x)/54
Annual Income = (35400 - x)/54 × 12/100 × 50
= Rs. (35400 - x)/9
According to the Question,
Annual Income from both Investments are equals.
∴ 9x/96 = (35400 - x)/9
1132800 - 32x = 27x
59x = 1132800
⇒ x = Rs. 19200
⇒ 35400 - x = Rs. 16200
Answer:
19200 & 16200
Step-by-step explanation:
Let say first Part = 100A
then Second Part = 35400 - 100A
A part invested at 9% rupees 100 shares at 4% discount
Share price = 100 - (4/100)100 = 96
Shares bought = 100A/96
Dividend received = (9/100)* 100 * (100A/96) = 75A/8
35400 - 100A invested 12% 50 shares at 8% premium
Share price = 50 + (8/100)*50 = 54
Shares bought = (35400 - 100A)/54
Dividend received = (12/100)*50 * (35400 - 100A)/54 = (35400 - 100A)/9
both dividends are equal
75A/8 = (35400 - 100A)/9
=> 675A = 35400 * 8 - 800A
=> 1475A = 35400 * 8
=> A = 24 * 8
=>A = 192
Part A = 100A = 19200
other part = 35400 - 19200 = 16200