Two numbers are in the ratio 2:3. If 9 is added to each they will be in the ratio 3:4, the numbers are ( 12, 28 (2) 18,27 (3)

Question

Two numbers are in the ratio 2:3. If 9 is added to
each they will be in the ratio 3:4, the numbers are
( 12,
28 (2) 18,27 (3) 8, 12 (4) 10, 15​

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Amara 6 days 2021-11-23T02:36:20+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-11-23T02:37:33+00:00

    Answer:

    (2) 18,27

    The numbers are

    First number = 18

    Second number = 27

    Step-by-step explanation:

    Given:

    • Two numbers are in the ratio 2:3

    • If 9 is added to each they will be in the ratio = 3:4

    Find :

    • The two numbers

    Solution :

    Let,

    First number = 2x

    Second number = 3x

    9 is added to each number

    So,

    First number = 2x + 9

    Second number = 3x + 9

    They will be in the ratio = 3:4

    According to question :

     \frac{2x + 9}{3x + 9}  \:  =  \:  \frac{3}{4}

    ⇒ 4 (2x + 9) = 3 (3x + 9)

    ⇒ 8x + 36 = 9x + 27

    ⇒ 8x – 9x = 27 – 36

    ⇒ – 1x = – 9

    ⇒ 1x = 9

    ⇒ x = 9

    First number = 2x

    ⇒ 2 (9)

    ⇒ 2 × 9

    ⇒ 18

    Second number = 3x

    ⇒ 3 (9)

    ⇒ 3 × 9

    ⇒ 27

    Therefore,

    First number = 18

    Second number = 27

    0
    2021-11-23T02:38:18+00:00

    \Large{\underline{\underline{\mathfrak{\bf{Solution}}}}}

    \Large{\underline{\mathfrak{\bf{Given}}}}

    • Two numbers are in the ratio 2:3
    • If 9 is added to each they will be in the ratio 3:4

    \Large{\underline{\underline{\mathfrak{\bf{Explanation}}}}}

    Let,

    • First Number = x
    • Second Number = y

    A/C to question,

    ==> x : y = 2 :3

    ==> x/y = 2/3

    ==> 3x – 2y = 0 (1)

    Again,

    ==> (x+9) : (y+9) = 3:4

    ==> (x+9)/(y+9) = 3/4

    ==> 4x – 3y = 27 – 36

    ==> 4x – 3y = – 9(2)

    Multiply by 4 in equ(1) & 3 in equ(2)

    • 12x – 8y = 0
    • 12x – 9y = -27

    ________________Sub. its

    ==> -8y + 9y = 27

    ==> y = 27

    keep value of y in equ(1)

    ==> 3x – 2*27 = 0

    ==> 3x = 54

    ==> x = 54/3

    ==> x = 18

    \Large{\underline{\underline{\mathfrak{\bf{Hence}}}}}

    • First Number be = 18
    • Second Number be = 27

    _________________

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