What is ‘A’ income?

The incomes of A and B are in the ratio 3:2 and their expenditure are in the ratio 5:3. If each saves Rs. 1000, A’s income is:

  1. Rs. 4000
  2. Rs. 5500
  3. Rs. 6000
  4. Rs. 3500
Monis Rasool Professor Asked on 25th October 2015 in Maths.
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  • 1 Answer(s)

    Answer: (3) Rs. 6000

    Explanation:-
    The ratio of the incomes of A and B = 3: 2
    Let the income of A = 3X and the income of B = 2X

    The ratio of their expenditure = 5: 3
    Then, let the expenditure of A = 5 Y and the expenditure of B = 3Y

    If each saves Rs. 1000,
    Then, 3 X – 5 Y = 1000 ……………… (1)
    2 X – 3 Y = 1000      ……………. (2)
    In equation (1) multiply by 2 & in equation  (2) multiply by 3,
    Then, 6 X – 10 Y = 2000       ………………… (3)
    6 X – 9 Y      = 3000       ……………………… (4)

    Subtract equation (4) from equation (3),
    Then, 6 X – 10 Y – 6 X + 9 Y = 2000 – 3000
    – Y = -1000
    Y = 1000

    Put the value of Y in equation (1),
    Then, 3 X – 5 x 1000 = 1000
    3 X – 5000 = 1000
    3 X = 1000 + 5000
    3 X = 6000
    X = 6000/3
    X = 2000

    Then, the income of A = 3 X = 3 x 2000
    = Rs. 6000

    Hence, the answer is (3) Rs. 6000.

    Anurag Mishra Professor Answered on 26th October 2015.
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