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The ratio of incomes of Venkanna and Saidulu is 7 : 5 and ratio of their expenditures is 3 : 2. If each person saves Rs. 3,000, then find the sum of their incomes.

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  1. Rs. 34000
  2. Rs. 32000
  3. Rs. 36000
  4. Rs. 30000

Answer (Detailed Solution Below)

Option 3 : Rs. 36000
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<p><strong>Given:</strong></p><p>Ratio of incomes of Venkanna and Saidulu = 7 : 5</p><p>Ratio of their expenditures = 3 : 2</p><p>Each person saves Rs. 3,000.</p><p><strong>Calculation:</strong></p><p>Let the incomes of Venkanna and Saidulu be 7x and 5x, respectively.</p><p>Let the expenditures of Venkanna and Saidulu be 3y and 2y, respectively.</p><p>Forming Equations:</p><p>Income - Expenditure = Savings</p><p>For Venkanna: 7x - 3y = 3000</p><p>For Saidulu: 5x - 2y = 3000</p><p>Solving for x and y:</p><p>Multiply the first equation by 2 and the second equation by 3:</p><p>2(7x - 3y) = 2(3000) → 14x - 6y = 6000</p><p>3(5x - 2y) = 3(3000) → 15x - 6y = 9000</p><p>Subtract the two equations:</p><p>(15x - 6y) - (14x - 6y) = 9000 - 6000</p><p>x = 3000</p><p>Finding Total Income:</p><p>Total income = 7x + 5x = 12x</p><p>⇒ 12 × 3000 = 36,000</p><p>Final Answer:</p><p>The sum of their incomes is <b>Rs. 36,000</b>.</p> - www.khautorepair.com
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