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

1. 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.

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.