Virat and Dhoni invest ₹36000 each in buying shares of two companies. Virat buys 15% ₹40 shares at a discount of 20%, while Dhoni buys ₹75 shares at a premium of 20%. If both receive equal dividends at the end of the year, find the rate percent of the dividend declared by Dhoni's company.

Total Investment of Virat = ₹36000

Nominal Value of Virat's shares = ₹40

As, Virat buys shares at 20% discount, Market Value of Virat's shares

$= ₹40 - 20\% \text{ of } ₹40 \\[0.5em] = ₹40 - ₹\Big(\dfrac{20}{100} \times 40 \Big) \\[0.5em] = ₹40 - ₹8 \\[0.5em] = ₹32$

No. of shares purchased by Virat

$= \dfrac{36000}{32} \\[0.5em] = 1125$

Rate of Dividend of Virat's shares = 15%

Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share

Annual Dividend of Virat

$= 1125 \times \dfrac{15}{100} \times 40 \\[0.5em] = ₹6750$

Let rate percent of the dividend declared by Dhoni's company be r%

Total Investment of Dhoni = ₹36000

Nominal Value of Dhoni's shares = ₹75

As, Dhoni buys shares at 20% premium, Market Value of Dhoni's shares

$= ₹75 + 20\% \text{ of } ₹75 \\[0.5em] = ₹75 + ₹\Big(\dfrac{20}{100} \times 75 \Big) \\[0.5em] = ₹75 + ₹15 \\[0.5em] = ₹90$

No. of shares purchased by Dhoni

$= \dfrac{36000}{90} \\[0.5em] = 400$

Annual Dividend of Dhoni

$= 400 \times \dfrac{r}{100} \times 75 \\[0.5em] = ₹300r$

As both Dhoni and Virat receive equal dividends,

$\therefore 300r = 6750 \\[0.5em] \Rightarrow r = \dfrac{6750}{300} \\[0.5em] \Rightarrow r = 22.5$

∴ Rate percent of the dividend declared by Dhoni's company = 22.5%