The Ratio 2x:3y Equals To :

If (x3-y³):(x2+xy+y2)=5:1 and (x2-y2):(x-y)=7:1, the ratio 2x:3y equals

  1. 4:1
  2. 3:2
  3. 2:3
  4. 4:3
Anurag Mishra Professor Asked on 25th October 2015 in Maths.
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  • 1 Answer(s)

    Answer: (1) 4: 1

    Explanation:-
    (x3 – y3): (x2 + xy + y2) = 5: 1
    (x – y) (x2 + y2 + xy)/ (x2 + y2 + xy) = 5/1
    (x – y)/1 = 5/1
    x – y = 5 ………………………… (1)

    And
    (x2 – y2): (x –y) = 7: 1
    (x – y) (x + y)/(x – y) = 7/1
    (x + y)/1 = 7/1
    x + y = 7 ………………………….. (2)
    Add equation (1) & (2),
    x – y + x + y = 5 + 7
    2 x = 12
    Then, x = 12/2 => x = 6

    Put the value of x in equation (1),
    Then, 6 – y = 5
    – y = 5 – 6
    – y = – 1
    y = 1
    Then, the value of 3 y = 3 x 1
    3 y = 3

    Therefore, 2x/3y = 12/3
    2x/3y = 4/1
    Then, the ratio 2x: 3y = 4: 1

    Hence, the answer is (1) 4: 1.

    Anurag Mishra Professor Answered on 26th October 2015.
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