Divide rs 50760 into two parts such that if one part is invested in 9%

1.	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» 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.