Question

    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'.
    A Rs. 34,000 Correct Answer Incorrect Answer
    B Rs. 43,400 Correct Answer Incorrect Answer
    C Rs. 43,980 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 'X' and 'Y' be Rs. '5m' and Rs. '6m', respectively. Let the savings of 'Y' be Rs. '8n'. Savings of 'X' = 1.30 Γ— 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 Γ— 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 Γ— 208n - 18.4n = 80000 Or, 2288n - 18.4n = 80000 So, n = (80000 / 2270) = 35.24 Or, 'm' = 208n = 208 Γ— 35.24 = 7330 Income of 'Y' = 6m = 6 Γ— 7330 = Rs.43,980

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