The three numbers are in the ratio 4:5:6. If the sum of the largest and
the smallest number is equal to the sum of the secon

The three numbers are in the ratio 4:5:6. If the sum of the largest and
the smallest number is equal to the sum of the second largest number
and 55. Find the numbers.

2 thoughts on “The three numbers are in the ratio 4:5:6. If the sum of the largest and<br /> the smallest number is equal to the sum of the secon”

  1. Answer:

    Given :-

    • The three numbers are in the ratio of 4 : 5 : 6.
    • The sum of the largest and the smallest number is equal to the sum of the second largest number and 55.

    To Find :-

    • What are the numbers.

    Solution :-

    Let,

    [tex]\mapsto[/tex] First number = 4x

    [tex]\mapsto[/tex] Second number = 5x

    [tex]\mapsto[/tex] Third number = 6x

    According to the question,

    [tex]\implies \sf 6x + 4x =\: 5x + 55[/tex]

    [tex]\implies \sf 10x =\: 5x + 55[/tex]

    [tex]\implies \sf 10x – 5x =\: 55[/tex]

    [tex]\implies \sf 5x =\: 55[/tex]

    [tex]\implies \sf x =\: \dfrac{\cancel{55}}{\cancel{5}}[/tex]

    [tex]\implies \sf x =\: \dfrac{11}{1}[/tex]

    [tex]\implies \sf\bold{\green{x =\: 11}}[/tex]

    Hence, the required numbers are :

    [tex]\dashrightarrow[/tex] First number :

    [tex]\leadsto \sf 4x[/tex]

    [tex]\leadsto \sf 4(11)[/tex]

    [tex]\leadsto \sf 4 \times 11[/tex]

    [tex]\leadsto \sf\bold{\red{44}}[/tex]

    [tex]\dashrightarrow[/tex] Second number :

    [tex]\leadsto \sf 5x[/tex]

    [tex]\leadsto \sf 5(11)[/tex]

    [tex]\leadsto\sf 5 \times 11[/tex]

    [tex]\leadsto \sf\bold{\red{55}}[/tex]

    [tex]\dashrightarrow[/tex] Third number :

    [tex]\leadsto \sf 6x[/tex]

    [tex]\leadsto \sf 6(11)[/tex]

    [tex]\leadsto \sf 6 \times 11[/tex]

    [tex]\leadsto \sf\bold{\red{66}}[/tex]

    [tex]\therefore[/tex] The numbers are 44 , 55 and 66 respectively.

    [tex]\rule{150}{2}[/tex]

    VERIFICATION :-

    [tex]\Rightarrow \sf 6x + 4x =\: 5x + 55[/tex]

    By putting x = 11 we get,

    [tex]\Rightarrow \sf 6(11) + 4(11) =\: 5(11) + 55[/tex]

    [tex]\Rightarrow \sf 66 + 44 =\: 55 + 55[/tex]

    [tex]\Rightarrow \sf\bold{\purple{110 =\: 110}}[/tex]

    Hence, Verified.

    [tex]\rule{150}{2}[/tex]

    #Learn more :

    3 Sum of three numbers which are in the ratio 3:4:5 is 60. What is the sum of their squares?

    (A)1970

    (B)1430

    (C)1250

    (D)1760

    https://brainly.in/question/40125762

  2. Provided: The three numbers are in the ratio 4:5:6. & sum of the largest and smallest number is equal to the sum of 2nd largest no. and 55.

    Need to find: The three respective numbers.

    ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀

    ❍ Let’s say, that the three numbers which are in the ratio be 4x, 5x and 6x.

    ⠀⠀⠀⠀

    [tex]\underline{\bigstar\:\pmb{ \frak{According \: to \: the \: given \: Question :}}}[/tex]

    • Given condition, if sum of the largest and smallest number is equal to the sum of 2nd largest no. and 55.

    [tex]:\implies\sf Largest \: no. + Smallest \: no. = 2nd \: largest \: no. + 55 \\\\\\:\implies\sf 6x + 4x = 5x + 55 \\\\\\:\implies\sf 10x = 5x + 55 \\\\\\:\implies\sf 10x – 5x = 55\\\\\\:\implies\sf 5x = 55\\\\\\:\implies\sf x = \cancel\dfrac{55}{5}\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 11}}}}}\;\bigstar[/tex]

    ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀

    Therefore,

    ⠀⠀⠀⠀

    • First no. 4x, 4(11) = 44
    • Second no. 5x, 5(11) = 55
    • Third no. 6x = 6(11) = 66

    ⠀⠀⠀⠀

    [tex]\therefore{\underline{\textsf{Hence, the three numbers are \textbf{44, 55 \sf{and} \textbf{66} \sf{respectively}.}}}}[/tex]⠀⠀⠀⠀

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