Question 31 (A) - CBSE Class 10 Sample Paper for 2026 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

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Question 31 (Choice A) The monthly income of Aryan and Babban are in the ratio 3 : 4 and their monthly expenditures are in ratio 5 : 7. If each saves ₹ 15,000 per month, find their monthly incomes.Given that Ratio of income of Ariyan and Babban persons is 3 : 4 Let Income of Aryan be 3x & Income for Babban be 4x Similarly, Ratio of expenditures of Ariyan and Babban is 5 : 7 Let Expenditure of Aryan be 5y & Expenditure of Aryan be 7y Now, Both save ₹ 15,000 per month We know that, Income – Expenditure = Savings For 1st person 3x – 5y = 15,000 Now, our equations are 3x – 5y = 15,000 …(1) 4x – 7y = 15,000 …(2) We will solve them by elimination We know that 12 is the multiple of 3 and 4 Multiplying (1) with 4 4 × (3x – 5y) = 4 × 15,000 12x – 20y = 60,000 Multiplying (2) with 3 3 × (4x – 7y) = 3 × 15,000 12x – 21y = 45,000 Now we use elimination with equation (3) & (4) y = 15,000 Putting value of x in (1) 3x – 5y = 15,000 3x – 5(15,000) = 15,000 3x – 75,000 = 15,000 3x = 15,000 + 75,000 3x = 90,000 x = (𝟗𝟎,𝟎𝟎𝟎)/𝟑 x = 30,000 Hence, x = 30,000, y = 15,000 is the solution of the equation. Hence, Monthly income of Aryan = 3x = 3 × 30,000 = ₹ 90,000 Monthly income of Babban = 4x = 4 × 30,000 = ₹ 1,20,000