The ratio of income of 'M' to that of 'N' is 4:5. Sum of their expenditures is Rs. 90,000. Savings of 'M' is 35% more than that of 'N'. Expenditure of 'M' is 50% of the sum of income of 'M' and 'N'. Find the income of 'N'.

ATQ, Let the income of 'M' and 'N' be Rs. '4p' and Rs. '5p', respectively. Let the savings of 'N' be Rs. '9q'. Savings of 'M' = 1.35 × 9q = Rs. '12.15q' Sum of expenditure of 'M' and 'N' = (4p - 12.15q) + (5p - 9q) = 90000 Or, 9p - 21.15q = 90000 ....(i) ATQ, 0.50 × 9p = 4p - 12.15q Or, 4.5p = 4p - 12.15q Or, 4p - 4.5p = 12.15q Or, -0.5p = 12.15q Or, p = (-12.15q / -0.5) = 24.3q Put the value of 'p' in equation (i), we get, 9 × 24.3q - 21.15q = 90000 Or, 218.7q - 21.15q = 90000 So, q = (90000 / 197.55) = 455.57 Or, 'p' = 24.3q = 24.3 × 455.57 = 11064 Income of 'N' = 5p = 5 × 11064 = Rs. 55,320