The ratio of incomes of X and Y is 5 : 4 and the ratio of their expenditures is 3 : 2. If both save Rs 1000 each, find the income of X (in Rs).

Explanation

​ Information Given: Ratio of incomes of X : Y = 5 : 4 Ratio of expenditures of X : Y = 3 : 2 Savings of both = Rs 1000 each Concept/Formula Used: Income − Expenditure = Saving Let incomes be 5x and 4x Let expenditures be 3y and 2y Explanation: For X: Income − Expenditure = Saving 5x − 3y = 1000 ……(1) For Y: 4x − 2y = 1000 ……(2) Multiply equation (2) by 3: 12x − 6y = 3000 ……(3) Multiply equation (1) by 2: 10x − 6y = 2000 ……(4) Subtract (4) from (3): (12x − 6y) − (10x − 6y) = 3000 − 2000 2x = 1000 x = 500 Income of X = 5x = 5 × 500 = Rs 2500