Question

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. Find the fraction.
INCERTI​

Answer 1

Step-by-step explanation:

$\frac{x + 2}{y + 2 } = \frac{9}{11 } \\ 11x + 22 = 9y + 18 \\ 11x - 9y + 4 = 0........1 \\ \frac{x + 3}{y + 3} = \frac{5}{6} \\ 6x + 18 = 5y + 15 \\ 6x - 5y + 3 = 0.................2 \\ by \: elimination \: method \\ y = 9 \\ x = 7 \\ thus \: the \: fraction \: is \: \frac{7}{9}$

Answer 2

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.