A man invests equal amounts of money in two companies A and B. Company A pays a dividend of 15% and its ₹ 100 shares are available at 20% discount. The shares of company B has a nominal value of ₹ 25 and are available at 20% premium. If at the end of one year, the man gets equal dividends from both the companies, find the rate of dividend paid by company B.

For company A,

Let invested money be ₹ x

Nominal value of each share (N.V.) = ₹ 100

Discount = 20%

M.V. of share = F.V. - Discount

= ₹ 100 - $\dfrac{20}{100} \times 100$

= ₹ 100 - ₹ 20 = ₹ 80.

No. of shares = $\dfrac{\text{Invested money}}{\text{M.V.}} = \dfrac{x}{80}$

Rate of dividend = 15%

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

= $\dfrac{x}{80} \times \dfrac{15}{100} \times 100$

= $\dfrac{3x}{16}$

For company B,

Let invested money be ₹ x

Nominal value of each share (N.V.) = ₹ 25

Premium = 20%

M.V. of share = N.V. + Premium

= ₹ 25 + $\dfrac{20}{100} \times 25$

= ₹ 25 + ₹ 5 = ₹ 30.

No. of shares = $\dfrac{\text{Invested money}}{\text{M.V.}} = \dfrac{x}{30}$

Let rate of dividend = d%

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

= $\dfrac{x}{30} \times \dfrac{d}{100} \times 25$

= $\dfrac{xd}{120}$

Since, man gets equal dividend from both companies so,

$\Rightarrow \dfrac{3x}{16} = \dfrac{xd}{120} \\[1em] \Rightarrow d = \dfrac{3x \times 120}{x \times 16} \\[1em] \Rightarrow d = \dfrac{360}{16} = 22.5 \%.$

Hence, dividend paid by company B = 22.5%.