Two numbers are in the ratio 9.4. If 7 is added to each of the numbers, the ratio becomes 5:3. Find the numbers.​

Question

Two numbers are in the ratio 9.4. If 7
is added to each of the numbers, the
ratio becomes 5:3. Find the numbers.​

in progress 0
Luna 4 weeks 2021-08-17T15:17:51+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-17T15:19:18+00:00

    Answer:

    18 and. 8

    Step-by-step explanation:

    As the ratio is 9:4, let the numbers are 9a and 4a.

    According to question: when 7 is added to both new numbers are 9a + 7 and 4a + 7.

    = > ( 9a + 7 ) : ( 4a + 7 ) = 5:3

    = > 3( 9a + 7 ) = 5( 4a + 7 )

    = > 27a + 21 = 20a + 35

    = > 27a – 20a = 35 – 21

    = > 7a = 14

    = > a = 14/7 = 2

    Hence the numbers are :

    9a = 9(2) = 18

    4a = 4(2) = 8

    0
    2021-08-17T15:19:33+00:00

    EXPLANATION.

    • GIVEN

    Two number are in the ratio = 9:4

    If 7 is added to each of the number, the ratio

    becomes = 5:3

    FIND THE NUMBER.

    According to the question,

    Let one number be = x

    Let another number be = y

    Case = 1

    Two numbers are in the ratio = 9:4

    => x/y = 9/4

    => 4x = 9y

    => 4x – 9y = 0 ……(1)

    Case = 2

    if 7 is added to the number the ratio = 5:3

    => x + 7 / y + 7 = 5/3

    => 3 ( x + 7 ) = 5 ( y + 7 )

    => 3x + 21 = 5y + 35

    => 3x – 5y = 14 …… (2)

    From equation (1) and (2) we get,

    multiply equation (1) by 3

    multiply equation (2) by 4

    we get,

    => 12x – 27y = 0

    => 12x – 20y = 14

    we get,

    => – 7y = -14

    => y = 2

    put the value of y = 2 in equation (2)

    we get,

    => 3x – 5y = 14

    => 3x – 5(2) = 14

    => 3x – 10 = 14

    => 3x = 24

    => x = 8

    Therefore,

    The number are = 8 and 2

Leave an answer

Browse
Browse

18:9+8+9*3-7:3-1*13 = ? ( )