Question

A 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. Find the fraction.
4​

Answer 1

Step-by-step explanation:

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.

Answer 2

Answer:

The fraction is 7/9.

Step-by-step explanation:

Given :-

• A 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.

To find :-

• The fraction.

Solution :-

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

According to the 1st condition,

• A fraction becomes 9/11 if 2 is added to both numerator and denominator.

$\to \sf \: \dfrac{x + 2}{y + 2} = \dfrac{9}{11} \\ \\ \to \sf \: 11x + 22 = 9y + 18 \\ \\ \to \sf \: 11x - 9y = 18 - 22 \\ \\ \to \sf \: 11x - 9y = - 4..........(i)$

According to the 2nd condition ,

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

$\to \sf \: \dfrac{x + 3}{y + 3} = \dfrac{5}{6} \\ \\ \to \sf \: 6x + 18 = 5y + 15 \\ \\ \to \sf \: 6x - 5y = - 3.........(i)$

Two equations are :

• 11x-9y=-4...........(i)×6
• 6x-5y=-3............(ii)×11

By elimination,

66x-54y=-24

66x-55y = -33

(-). (+). (+)

_____________

y = 9

Now put y = 9 in eq(ii)

6x-5y=-3

→ 6x - 5×9 = -3

→ 6x = -3 + 45

→ x = 42/6

→ x = 7

Therefore,

• The fraction = 7/9