Question

Divide 50,760 into two parts such that if one part is invested in 8% Rs.100 shares at 8% discount and the other in 9% Rs.100 shares at 8% premium, the annual incomes from both the investments are equal.
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Answer 1

Let we divide Rs.50760 in two parts 

One is Rs.x and another is Rs.(50760-x)

The share bought with Rs.x  were bought at 8% discount=100−1008×100=Rs.92

No of share bought with Rs.x=92x

As income =No. of share×dividend ×face value

Dividend =8%

Face value=100

∴ Income=92x×1008×100=928x (income 1)

The buying price of share bought with Rs.(50760-x) at 8% premium=100+1008=100108

No of share bought with Rs.(50760-x)=10850760−x

Dividend=9%

Face value=100

∴ Income=10850760−x×1009×100=1250760−x   (income 2)

According to the question both incomes are equal

⇒928x=1250760−x

⇒24x=23(50760−x)

⇒47x=50760×23

⇒x=47

Answer 2

Question:-

Divide 50,760 into two parts such that if one part is invested in 8% Rs.100 shares at 8% discount and the other in 9% Rs.100 shares at 8% premium, the annual incomes from both the investments are equal.

Solution:-

• Total investment = ₹50,760.
• Let first part of investment = x.
• Then second part = ₹50,760 – x.
• Rate of divided in first part = 8% ₹100 at discount = 8%.

• ∴ M.V. of each share = ₹100 – 8 = ₹92
• Rate of dividend second part = 9% ₹100 at premium = 8%.
• ∴ M.V. of each share = 100 + 8 = ₹108.
• But, annual income from both part is same.

$\sf{∴x \times \frac{8}{92} (50760 - x) \times \frac{9}{108} }$

$\sf{ = > \frac{8x}{92} = \frac{50760 - x}{12} }$

$\sf{ = > \frac{12 \times 8x}{92} = 50760 - x}$

$\sf{ = > \frac{24}{23x} + x = 50760}$

$\sf{ = > \frac{47x}{23} = 50760}$

$\sf{ = > x = \frac{50760 \times 23}{47} = 23 \times 1080} = ₹24840$

• First part = ₹24,840.
• and Second part = ₹50,760 – ₹24,840 = ₹25,920.

Answer:-

• First part = ₹24,840.
• Second part = ₹25,920.