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    Two numbers are in the ratio 9 : 5. If 9 is added to the greater number and 5 is subtracted from the smaller number, the greater number becomes thrice
    Question

    Two numbers are in the ratio 9 : 5. If 9 is added to the greater number and 5 is subtracted from the smaller number, the greater number becomes thrice the smaller one. Find the numbers.

    A.

    36, 10

    B.

    72, 40

    C.

    18, 10

    D.

    36, 20

    Correct option is D

    Given:

    Two numbers are in the ratio 9 : 5.

    9 is added to the greater number.

    5 is subtracted from the smaller number.

    The greater number becomes thrice the smaller number.

    Solution:

    ​Let the numbers be 9x and 5x, where x is a common factor.

    ​According to the problem, 9x + 9 = 3(5x - 5)

    ​15x - 9x = 9 + 15

    6x = 24

    x = 4

    ​Greater number: 9x = 9 ×\times​ 4 = 36

    Smaller number: 5x = 5 ×\times 4 = 20 

    Therefore, the numbers are 36 and 20.

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