If 3^(x+y) =81 and 81^(x-y)=3, then the value of x/y is

(a) 15/34
(b) 15/17
(c) 17/15
(d) 17/30

Anurag Mishra Professor Asked on 27th March 2016 in Maths.
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  • 1 Answer(s)

    Answer: (c) 17/15

    Solution:-
    3^(x + y) = 81
    3^(x + y) = 3^4
    Comparing on both side,
    X + Y = 4 ………….. (1)

    81^(x – y) = 3
    3^4(x – y) = 3^1
    Comparing on both side,
    4 x – 4 y = 1 …………… (2)

    In equation(1) multiply by 4,
    Then, 4 X + 4 Y = 16  …………. (3)

    Add equation (1) & (2),
    Then, 4 X – 4 Y + 4 X + 4 Y = 16 + 1
    8 X = 17
    X = 17/8

    Put the value of X = 17/8 equation (1),
    17/8 + Y = 4
    Y = 4 – 17/8
    Y = (32 –  17)/8
    Y = 15/8

    Then, the ratio of X/Y = 17 x 8/15 x 8
    = 17/15

    Hence, the correct answer is option (c) 17/15.

    Anurag Mishra Professor Answered on 27th March 2016.
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