Question

Divide rs 50760 into two parts such that if one part is invested in 9%, rs 100 shares at 8% dis and the other in 8%, 100 shares at 8% premium, the annual incomes from both the investment are equal

Answer 1

Given :

The Invested amount (in two parts) = ₹ 50,760

Face value of first part = ₹100

Dividend = 9%

Discount = 8%

Face value of second part = ₹100

Dividend = 8%

Premium = 8%

To find :

The amount of both the investment.

Solution :

Let we divide the amount in two parts.

First part be 'x' so the other part = (50760-x)

The first part of shares bought with Rs. x at the discount of 8%.

Market value of one share of first part   = 100 - (8% of 100)

                                                                  = 100 - 8

                                                                  = ₹92

Number of shares = $\frac{\text{total invested amount}}{\text{MV of one share}}$

                              = $\frac{x}{92}$

Income from first part = No. of shares × dividend × face value

                                    = $\frac{x}{92}\times \frac{9}{100}\times 100$

                                     = $\frac{9x}{92}$

Second part of shares bought with Rs. 50760-x at the premium of 8%.

Market value of one share of second part = 100 +(8% of 100)

                                                                      = 100 + 8

                                                                      = Rs. 108

Number of shares = $\frac{50760-x}{108}$

Income from second part of investment =  $\frac{50760-x}{108}\times \frac{8}{100}\times 100$

                                                                  =  $\frac{-2}{27}x+3760$

According to question income from both parts are equal.

$\frac{9x}{92}=\frac{-2}{27}x+3760$   [add 2/27x both side]

$\frac{427}{2484}x=3760$         [multiply 427/2484 both side]

x = 21873.16

First part of investment = 21873.16

so the other part of investment = 50760 - 21873.16

                                                    = 28886.84

First part of investment is 21873.16 and the other part is 28886.84.