the ratio of two numbers is 5:9. If each of the numbers are increased by 10 the ratio becomes 10:17. Find the numbers.​

Question

the ratio of two numbers is 5:9. If each of the numbers are increased by 10 the ratio becomes 10:17. Find the numbers.​

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Adalyn 1 month 2021-08-18T23:00:20+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-18T23:01:43+00:00

    Answer :

    Given :

    • Ratio of two numbers = 5:9

    • Final Ratio of no(s) = 10:17 (when inc. by 10)

    To Find :

    • Numbers

    Solution :

    • Let the number be x . Now , the numbers are 5x and 9x .

    • If each number is increased by 10 :

    \implies \sf 5x\:+\:10 \\

    \implies \sf 9x\:+\:10 \\ \\

    According to the question :

    → If we increase both the numbers by 10 the ratio becomes 10:17 .

    \implies \sf \dfrac{5x\:+\:10}{9x\:+\:10}\:=\: \dfrac{10}{17} \\ \\

    Now , solving further :

    \implies \small \sf 17(5x\:+\:10)\:=\:10(9x\:+\:10) \\

    \implies \small \sf 85x\:+\:170\:=\:90x\:+\:100 \\

    \implies \small \sf 90x\:-\:85x\:=\:170\:-\:100 \\

    \implies \small \sf 5x\:=\:70 \\

    \implies \small \sf x\:=\: \dfrac{70}{5} \\

    \implies \large{\underline{\sf{\red{x\:=\: 14}}}} \\ \\

    • Numbers are : 70 and 126

    \implies \sf 5x\:=\:5(14)\:=\:70 \\

    \implies \sf 9x\:=\:9(14)\:=\:126 \\

    _____________________

    0
    2021-08-18T23:01:47+00:00

    Step-by-step explanation:

    Solution:-

    Let the common ratio between the numbers be x

    As, the ratio of two numbers is 5 : 9

    The first number = 5x

    The second number = 9x

    If the number is increased by 10

    The first number becomes = 5x + 10

    The second number becomes = 9x + 10

    The ratio becomes 10 : 17

    So:-

     \rm \dfrac{5x + 10}{9x + 10}  =  \dfrac{10}{17}

    By cross multiplication:-

    → 17(5x + 10) = 10(9x + 10)

    → 85x + 170 = 90x + 100

    → 90x – 85x = 170 – 100

    → 5x = 70

    → x = \dfrac{70}{5}

    → x = 14

    The first number = 5x = 5 × 14 = 70

    The second number = 9x = 9 × 14 = 126

    The number are 70 and 126

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