Question

14. Divider
35400 into two parts such that if one part is invested in 9%, 100 shares at 4% discount
the other in 129, 50 shares at 8% premium, the annual incomes are equal.
350760 into two parts such that if one part is invested in S%, 100 shares at 8%
aunt and the other in 9%, 100 shares at 8% premium, the annual incomes from both the
15. Divide 750760 inta
investments are equal.​

Answer 1

$\huge{\underline{\mathfrak{Solution:-}}}$

★ Given:-

Let the two parts in which Rs.35400  is to be divided be Rs. x and Rs.(35400  - x).

$\huge{\underline{\mathfrak{Solution:-}}}$

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

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