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

Example 11 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 2
Example 11 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 3 Example 11 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 4 Example 11 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 5

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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. Given that Ratio of income of two persons is 9 : 7 Let 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 Now, Both save 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) = 3(2000) 27x – 12y = 6000 Multiplying (2) with 4 4(7x – 3y) = 4(2000) 28x – 12y = 8000 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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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.