the sum of the numerator and denominator of a fraction is 12vif 1 is added to numerator and 3 is to denominator the difference will become –

Question

the sum of the numerator and denominator of a fraction is 12vif 1 is added to numerator and 3 is to denominator the difference will become -4 find the fraction​

in progress 0
Audrey 1 month 2021-08-13T08:35:46+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-13T08:36:47+00:00

    Correct Question :

    The sum of the numerator and denominator of a fraction is 12. if 1 is added to numerator and 3 is to denominator then, the difference will become -4. Find the fraction.

    Solution :

    ☯️ Let,

    The Numerator be x.

    The Denominator be y.

    According To The Question,

    \sf{x + y = 12.....(1)}

    \to\sf{ \dfrac{x + 1}{y + 3}  =  - 4}\\

    \to \sf{x + 1 =  - 4(y + 3)} \\

    \to\sf{x + 1 =  - 4y - 12} \\

    \to\sf{x + 4y =  - 13.....(2)} \\

    From 1] and 2],

    \dashrightarrow\sf{ - 3y = 25} \\

    \dashrightarrow\boxed{\sf{y =  -  \dfrac{25}{3} }} \\

    Now,

    \dashrightarrow\sf{x -  \dfrac{25}{3} = 12} \\

    \dashrightarrow\boxed{\sf{x =  \dfrac{61}{3}} }\\

    Now, Fraction :-

    \boxed{\bf\pink{ \dfrac{x}{y} =   -   \dfrac{61}{25}}}

    0
    2021-08-13T08:36:51+00:00

    EXPLANATION.

    Let the numerator of fraction be = x

    Let the denominator of fraction be = y

    Sum of the numerator and denominator of a

    fraction = 12.

    => x + y = 12 …….(1)

    If 1 is added to numerator and 3 is to denominator

    The fraction will become = 4.

    => x + 1 / y + 3 = -4

    => x + 1 = -4 ( y + 3 )

    => x + 1 = -4y – 12

    => x + 4y = -13 ……(2)

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

    => -3y = 25

    => y = -25/3

    put the value of y = -25/3 in equation (1)

    => x – 25/3 = 12

    => x = 12 + 25/3

    => x = 36 + 25 / 3

    => x = 61/3

    Therefore,

    => Fraction be = x/y = 61/3 / – 25/3 = -61/25.

Leave an answer

Browse
Browse

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