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    Question

    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'.
    A Rs. 55,320 Correct Answer Incorrect Answer
    B Rs. 43,400 Correct Answer Incorrect Answer
    C Rs. 53,980 Correct Answer Incorrect Answer
    D Rs. 41,200 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    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

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