Question

A man invests equal sum of money in two firms paying 8% shares(rs 100) at a premium of rs 25 and 6% shares (rs 100) at a discount of rs 25.he finds that if with his total investment he had bought equal number of shares of each company,his income would have been rs 142 less.find his total investment.

Answer 1

accountancy ........

Answer 2

"A man invest Rs x in one company.

Concern A:

Investment = Rs X

Normal value of each share = Rs 100

As per market value of each share = Rs 125

No. of shares bought = $\frac { x }{ 125 }$

Rate of dividend = 8 percentage

Dividend of one share = 8 % of Rs 100 = Rs 8

Dividend on $\frac { x }{ 125 } shares = Rs \frac { 8x }{ 125 }$

For Concern B:

Investment = Rs x

Normal value of each share = Rs 100

As per market value of each share = Rs 75

No of shares bought =$\frac { x }{ 75 }$

Rate of dividend = 6 percentage

Dividend on one share = 6% of Rs 100 = Rs 6

Dividend on X/75 shares = $Rs \frac { 6x }{ 75 }$

All over total income $= \frac { 8x }{ 125 } \quad +\quad \frac { 6x }{ 75 } \quad =\quad Rs\quad \frac { 18x }{ 125 }$

Let n be the number of shares bought of each concern.

Net Total Investment = Rs 2x

As per market value of one share of concern A = Rs 125

As per market value of one share of concern B = Rs 75

As per given situation,

125n + 75n = 2x

$\Rightarrow \quad n\quad =\quad \frac { x }{ 100 }$

Dividend on one share of concern A = Rs 8

Dividend on $\frac { x }{ 100 }$ share of concern $A = Rs \frac { 8x }{ 100 }$

Dividend on one shares of company B = Rs 6

Dividend on $\frac { x }{ 100 }$ shares of company $B = Rs \frac { 6x }{ 100 }$

$Total\quad Income\quad =\quad \frac { 8x }{ 100 } \quad +\quad \frac { 6x }{ 100 } \quad =\quad \frac { 14x }{ 100 }$

According to question,

$\frac { 18x }{ 125 } \quad -\quad \frac { 14x }{ 100 } \quad =\quad 142$

0.144x - 0.14x = 142

0.004x = 142

x = 35500

$Total\quad invested\quad money\quad =\quad Rs.2x\quad =\quad Rs.2\quad \times \quad 35500\quad =\quad Rs.71000$"