Question

Sachin and Dhoni invest Rs. 36,000 each in buying shares of two companies. Sachin buys 15% Rs. 40 shares at a discount of 20%, while Dhoni buy Rs. 75 share at a premium of 20%. If both receive equal dividend at the end of the year, find the rate percent of dividend declared by Dhoni company.

Answer 1

Step 1: Given information,

Sachin invested$=\mathrm{Rs}.36,000$

Dhoni invested$=\mathrm{Rs}.36,000$

Sachin buys$15\%\mathrm{Rs}.40$ shares at a discount of $20\%$.

Dhoni buys $\mathrm{Rs}.75$shares at a premium of $20\%$.

Step 2: Calculate the dividend received by Sachin:

Sachin invested $=\mathrm{Rs}.36,000$
Share price$=\mathrm{Rs}.40$

Since Sachin buys $15\%\mathrm{Rs}.40$shares at a discount of$20\%$,

$\begin{array}{rcl}\mathrm{Dividend}\mathrm{per}\mathrm{share}& =& \frac{15}{100}\times 40\\ & =& \mathrm{Rs}.6\end{array}$

Now,

$\mathrm{Discount}=20\%$

Thus,

$\begin{array}{rcl}\mathrm{Cost}\mathrm{price}\mathrm{of}\mathrm{a}\mathrm{share}& =& 40-\left(\frac{20}{100}\times 40\right)\\ & =& \mathrm{Rs}.32\end{array}$

The number of shares bought by Sachin is computed as:

$\begin{array}{rcl}\mathrm{Number}\mathrm{of}\mathrm{shares}& =& \frac{36,000}{32}\\ & =& 1,125\end{array}$

Dividend received by Sachin $=1125\times 6=\mathrm{Rs}.6750$

Step 3: Calculate the dividend received by Dhoni:

Dhoni invested$=\mathrm{Rs}.36,000$

Let us consider that the dividend is $x\%$. Then,

$\begin{array}{rcl}\mathrm{Dividend}\mathrm{per}\mathrm{share}& =& \frac{x}{100}\times 75\\ & =& \frac{3}{4}x\end{array}$

Now,

$\mathrm{Premium}=20\%$

Calculate cost price of share.

$\begin{array}{rcl}\mathrm{Cost}\mathrm{price}\mathrm{of}\mathrm{share}& =& 75+\left(\frac{20}{100}\times 75\right)\\ & =& \mathrm{Rs}.90\end{array}$

The number of shares bought by Dhoni is computed as:

$\begin{array}{rcl}\mathrm{Number}\mathrm{of}\mathrm{shares}& =& \frac{36,000}{90}\\ & =& 400\end{array}$

Calculate dividend received by Dhoni.

$\begin{array}{rcl}\mathrm{Dividend}\mathrm{received}\mathrm{by}\mathrm{Dhoni}& =& \left(\frac{3}{4}x\right)\times 400\\ & =& 300x\end{array}$

Since, Sachin and Dhoni received equal dividends.

$\begin{array}{rcl}300x& =& 6,750\\ & \Rightarrow & x=\frac{6,750}{300}\\ \therefore x& =& 22.5\end{array}$

Hence, the rate of dividend declared by Dhoni's company is $22.5\%$.