3. A fraction becomes 9/11, if 2 is added to both the numerator and denominator. If 3 is added to both the numerator and denominat

Question

3. A fraction becomes 9/11,
if 2 is added to both the numerator and denominator. If 3 is added to
both the numerator and denominator it becomes
5/6
Find the fraction.​

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Jasmine 3 days 2021-10-11T09:17:46+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-11T09:19:12+00:00

    Information :- This solution is based on Cross Multiplication.

    Given :-

    Fraction becomes 9/11 if 2 is added to both numerator and denominator.

    If 3 is added to both numerator and denominator it becomes 5/6.

    Solution :-

    Let the Numerator be x                  

    Let the Denominator be y                  

    Fraction = x/y                  

    According to the Question,                  

    ⇒ (x + 2)/y + 2 = 9/11                  

    On Cross multiplying,                  

    ⇒ 11x + 22 = 9y + 18                  

    Subtracting 22 from both sides,                  

    ⇒ 11x = 9y – 4                  

    Dividing by 11, we get                  

    ⇒ x = 9y – 4/11 … (i)                  

    Then,              

    ⇒ (x+3)/y +3 = 5/6 … (ii)                  

    On Cross multiplying,                  

    ⇒ 6x + 18 = 5y + 15                  

    Subtracting the value of x, we get                  

    ⇒ 6(9y – 4 )/11 + 18 = 5y + 15                  

    Subtracting 18 from both the sides                  

    ⇒ 6(9y – 4 )/11 = 5y – 3                  

    ⇒ 54 – 24 = 55y – 33                  

    ⇒ –y = – 9                  

    ⇒ y = 9                  

    Putting this value of y in equation (i), we get                  

    ⇒ x = 9y – 4                  

    ⇒ x = (81 – 4)/77                  

    ⇒ x = 77/11                  

    ⇒ x = 7                  

    Hence, the  fraction is 7/9.

    0
    2021-10-11T09:19:35+00:00

    Answer:

    Let the numerator and denominator be x and y respectively.

    Therefore, the required fraction will be x/y

    According to Question now,

    ➳ (x + 2)/(y + 2) = 9/11

    ➳ 11(x + 2) = 9(y + 2)

    ➳ 11x + 22 = 9y + 18

    ➳ 22 – 18 = 9y – 11x

    ➳ 4 = 9y – 11x

    ➳ 11x = 9y – 4

    ➳ x = 9y – 4/11…….[Equation (i)]

    Now, it is given that 3 is added to both numerator and denominator it becomes 5/6 :]

    ➳ (x + 3)/(y + 3) = 5/6

    ➳ (x + 3)6 = 5(y + 3)

    ➳ 6x + 18 = 5y + 15

    ➳ 6x – 5y + 18 – 15 = 0

    ➳ 6x – 5y + 3 = 0

    ➳ 6(9y – 4)/11 – 5y + 3 = 0

    ➳ 54y – 24/11 = 5y – 3

    ➳ 54y – 24 = 11(5y – 3)

    ➳ 54y – 24 = 55y – 33

    ➳ -24 + 33 = 55y – 54y

    ➳ 9 = y

    Now, Putting y = 9 in equation (i) we get,

    ➳ x = 9y – 4/11

    ➳ x = 9(9) – 4/11

    ➳ x = 81 – 4/11

    ➳ x = 77/11

    ➳ x = 7

    Therefore, the required fraction is 7/9.

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