Three numbers are in ratio 3:4:5 and the sum of their cubes is 1728000. Find the numbers.​

Question

Three numbers are in ratio 3:4:5 and the sum of their cubes is 1728000. Find the numbers.​

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Athena 1 month 2021-08-12T06:59:55+00:00 1 Answer 0 views 0

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    2021-08-12T07:00:58+00:00

    \large\underline{\underline\mathrm\green{QUESTION}}

    Three numbers are in ratio 3:4:5 and the sum of their cubes is 1728000. Find the numbers.

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    \large\underline{\underline\mathrm\pink{SOLUTION}}

    GIVEN

    • The number are in the ratio 3:4:5.
    • Sum of their cubes = 1728000

    TO FIND

    • The Numbers.

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    Let, The Numbers be 3x, 4x and 5x

    ACCORDING TO QUESTION

    \bold{\implies (3x)³+(4x)³+(5x)³ = 172800}

    \bold{\implies 27x³ + 64x³ +125x³ = 1728000}

    \bold{\implies 216x³ =1728000}

    \bold{\implies x³ =8000}

    \bold{\implies x = \sqrt[3]{8000}}

    \bold{\implies x = 20}

    THEREFORE

    • 3x = 3×20 = 60
    • 4x = 4×20 = 80
    • 5x = 5×20 = 100

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