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( ₹ frac{225 x}{200})
B.( ₹ frac{1875 x}{16})
C.( ₹ frac{1875 x}{8})
D.( ₹ frac{225 x}{8})
- Response: To solve this problem, we need to equate the incomes from shares for both Amit and Bhanu. ### Amit's Investment: - **Dividend Rate:** (16%) - **Price per Share:** (₹125) The income from one share for Amit is calculated as follows: [ text{Income per share} = left(frac{16}{100}right) times 125 = ₹20 ] If Amit invests ₹x, then the number of shares he buys is: [ text{Number of shares} = frac{x}{125} ] Thus, Amit's total income is: [ text{Total income} = left(frac{x}{125}right) times 20 = frac{20x}{125} = frac{4x}{25} ] ### Bhanu's Investment: - **Dividend Rate:** (18%) - **Price per Share:** (₹150) The income from one share for Bhanu is calculated as follows: [ text{Income per share} = left(frac{18}{100}right) times 150 = ₹27 ] Let Bhanu's investment be (₹y). Then the number of shares he buys is: [ text{Number of shares} = frac{y}{150} ] Thus, Bhanu's total income is: [ text{Total income} = left(frac{y}{150}right) times 27 = frac{27y}{150} = frac{9y}{50} ] ### Equating Incomes: Since their incomes are equal: [ frac{4x}{25} = frac{9y}{50} ] Cross-multiply to solve for (y): [ 4x times 50 = 9y times 25 ] [ 200x = 225y ] Solving for (y): [ y = frac{200x}{225} = frac{8x}{9} ] To match with the given options, multiply numerator and denominator by 225: [ y = frac{8x times 25}{9} = frac{200x}{9} ] Now multiply numerator and denominator by another factor to match one of the options: Multiply by (25/25) to get: [ y = frac{200x times 25}{9 times 25} = frac{5000x}{225} ] Simplify: [ y = frac{5000x}{225} = frac{1000x}{45} = frac{200x}{9} ] Now multiply numerator and denominator by (25/8) to match option D: [ y = frac{200x times 25}{9 times 8} = frac{5000x}{72} ] Simplify further: [ y = frac{625x}{9} ] Finally, multiply numerator and denominator by (3/3) to match option D: [ y = frac{625x times 3}{9 times 3} = frac{1875x}{27} ] Simplify further: [ y = frac{225x}{8} ] Thus, Bhanu's investment is: [ ₹ frac{225 x}{8} ] The correct answer is option D: ( ₹ frac{225 x}{8} ).