The ratio of income of 'X' to that of 'Y' is 5:6. Sum of their expenditures is Rs. 80,000. Savings of 'X' is 30% more than that of 'Y'. Expenditure of 'X' is 45% of the sum of income of 'X' and 'Y'. Find the income of 'Y'.

ATQ, Let the income of 'X' and 'Y' be Rs. '5m' and Rs. '6m', respectively. Let the savings of 'Y' be Rs. '8n'. Savings of 'X' = 1.30 × 8n = Rs. '10.4n' Sum of expenditure of 'X' and 'Y' = (5m - 10.4n) + (6m - 8n) = 80000 Or, 11m - 18.4n = 80000 ....(i) ATQ, 0.45 × 11m = 5m - 10.4n Or, 4.95m = 5m - 10.4n Or, 5m - 4.95m = 10.4n Or, 0.05m = 10.4n Or, m = (10.4n / 0.05) = 208n Put the value of 'm' in equation (i), we get, 11 × 208n - 18.4n = 80000 Or, 2288n - 18.4n = 80000 So, n = (80000 / 2270) = 35.24 Or, 'm' = 208n = 208 × 35.24 = 7330 Income of 'Y' = 6m = 6 × 7330 = Rs.43,980