By purchasing ₹50 gas shares for ₹80 each, a man gets 4% profit on his investment. What rate percent is company paying? What is his dividend if he buys 200 shares?

Let the rate percent company is paying be x%

Dividend on 1 share of ₹50

$= \text{x\% of ₹50} \\[0.5em] = \dfrac{x}{100} \times 50 \\[0.5em] = \dfrac{x}{2}$

His profit on one share

$= \text{4\% of ₹80} \\[0.5em] = \dfrac{4}{100} \times 80 \\[0.5em] = \dfrac{32}{10} \\[0.5em] = \dfrac{16}{5}$

As per the given,

$\dfrac{x}{2} = \dfrac{16}{5} \\[0.5em] \Rightarrow x = \dfrac{16 \times 2}{5} \\[0.5em] \Rightarrow x = 6.4$

∴ Rate percent company is paying = 6.4%

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

$= 200 \times \dfrac{6.4}{100} \times 50 \\[0.5em] = 200 \times \dfrac{64}{1000} \times 50 \\[0.5em] = 2 \times 64 \times 5 \\[0.5em] = \bold{₹640}$

∴ Dividend if he buys 200 shares = ₹640