A sum of ₹ 54000 is invested partly in shares paying 6% dividend at 40% premium and partly in 5% shares at 25% premium. If the nominal value of one share in each company is ₹ 100 and the total income of the man is ₹ 2,240, find the money invested in the second company.

For first company,

Let money invested be ₹ x.

N.V. = ₹ 100

Premium = 40%

M.V. = N.V. + Premium

= 100 + $\dfrac{40}{100} \times 100$

= ₹ 100 + ₹ 40

= ₹ 140.

No. of shares = $\dfrac{\text{Invested money}}{\text{M.V.}} = \dfrac{x}{140}$

Rate of dividend = 6%

Total dividend for first company = No. of shares × Dividend × 100

= $\dfrac{x}{140} \times \dfrac{6}{100} \times 100$

= $\dfrac{3x}{70}$

For second company,

Let money invested be ₹ (54000 - x).

N.V. = ₹ 100

Premium = 25%

M.V. = N.V. + Premium

= 100 + $\dfrac{25}{100} \times 100$

= ₹ 100 + ₹ 25

= ₹ 125.

No. of shares = $\dfrac{\text{Invested money}}{\text{M.V.}} = \dfrac{54000 - x}{125}$

Rate of dividend = 5%

Total dividend for second company = No. of shares × Dividend × 100

= $\dfrac{54000 - x}{125} \times \dfrac{5}{100} \times 100$

= $\dfrac{54000 - x}{25}$

Since, total income = ₹ 2240

$\therefore \dfrac{54000 - x}{25} + \dfrac{3x}{70} = 2240 \\[1em] \Rightarrow \dfrac{14(54000 - x) + 3x \times 5}{350} = 2240 \\[1em] \Rightarrow \dfrac{756000 - 14x + 15x}{350} = 2240 \\[1em] \Rightarrow 756000 + x = 2240 \times 350 \\[1em] \Rightarrow 756000 + x = 784000 \\[1em] \Rightarrow x = 784000 - 756000 = 28000.$

₹ (54000 - x) = ₹ 54000 - ₹ 28000 = ₹ 26000.

Hence, money invested in second company = ₹ 26000.