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Example 11 - Ratio of incomes of two persons is 9 : 7 - Elimination

  1. Chapter 3 Class 10 Pair of Linear Equations in Two Variables
  2. Serial order wise
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Example 11 The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save Rs.2000 per month, find their monthly incomes. It is given that , Ratio of income of two persons is 9:7 Let the income of 1st person be 9x & income for 2nd person be 7x. Similarly, Ratio of expenditures of two persons is 4 : 3 Let expenditure of 1st person be 4y & expenditure of 2nd person be 3y Both saves Rs 2000 per month Both saves Rs 2000 per month We know that, Income – Expenditure = Savings For 1st person 9x – 4y = 2000 Similarly for 2nd person 7x – 3y = 2000 Now, our equations are 9x – 4y = 2000 …(1) 7x – 3y = 2000 …(2) We will solve them by elimination We know that 12 is the multiple of 3 and 4 Multiplying (1) with 3 3 ( 9x – 4y) = 2000×3 27x – 12y = 6000 Now we use elimination with equation (3) & (4) –x = – 2000 x = 2000 Putting value of x in (1) 9x – 4y = 2000 9(2000) – 4y = 2000 18000 – 4y = 2000 - 4y = 2000 – 18000 - 4y = - 16000 y = 16000/4 y = 4000 Hence, x = 2000, y = 4000 is the solution of the equation . Hence, Monthly income of 1st person = 9x = 9 ×2000 = Rs 18,000 Monthly income of 2nd person = 7x = 7 ×2000 = Rs 14,000

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