Question

A fraction becomes $\frac{9}{11}$ if 2 is added to both numerator and the denominator. If 3 is added to both the numerator and the denominator it becomes $\frac{5}{6}$. Find the fraction.

Answer 1

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

 

Solution:

Let the numerator and denominator of the fraction be x and y.  

Then , fraction =   numerator / denominator = x/y

Condition : 1

x+2/y+2 = 9/11

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

11x + 22 = 9y + 18

11x – 9y = 18 – 22  

11x – 9y + 4 = 0

11x – 9y = - 4 ……….(1)

 

Condition : 2

x + 3/ y + 3 = 5/6

6(x + 3) = 5(y + 3)

6(x + 3) = 5(y + 3)

6x + 18 = 5y + 15

6x – 5y = 15 –18

6x – 5y + 3 = 0

6x – 5y =  - 3

6x = - 3 + 5y

6x = 5y - 3

x = (5y - 3)/6 ………..(2)

On Substituting the value of x in equation (1) we obtain :  

11x - 9y = - 4

11(5y - 3)/6 - 9y = - 4

(55y - 33)/6 - 9y = - 4

[(55y - 33) - 6 × 9y]/6 = - 4

[(55y - 33) - 54y] = - 4 × 6

[55y - 33- 54y] = - 24

y - 33 = - 24

y = - 24 + 33

y = 9

On putting y = 9 in eq (2)  we obtain :

x = (5y - 3)/6

x = (5 × 9 - 3)/6

x = (45 - 3)/6

x = 42/6

x = 7

Now , fraction =  x/y = 7/9

Hence, the fraction is 7/9.

Hope this answer will help you…

 

Some more questions from this chapter :  

The denominator of a fraction is 1 more than twice its numerator. If the sum of the fraction and its reciprocal is 34/15. Find the fraction.

(Class 10 Maths Sample Question Paper)

https://brainly.in/question/2368643

 

The numerator of a fraction is 4 less than the denominator. If the numerator is decreased by 2 and denominator is increased by 1, then the denominator is eight times the numerator. Find the fraction.

https://brainly.in/question/17207998

Answer 2

Answer:

Step-by-step explanation:

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.