Question

5. A fraction becomes9/11 ,if 2 is added to both the numerator and denominator. If 3 is added to both the numerator and the denominator, it becomes 5/6

Find the fraction. ​

Answer 1

Answer:

11/13 and 8/9

Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation:

Let the fraction be ( x / y ).

If 2 is added to both the numerator and denominator, it becomes 9 / 11.

So, ( x + 2) / ( y + 2 ) = 9 / 11

⇒ 11 (x + 2 ) = 9 ( y + 2 )

⇒ 11x + 22 = 9y + 18----eq ( 1 ) ( say ).

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

So, ( x + 3 ) / ( y + 3 ) = 5 / 6

⇒ 6 ( x + 3 ) = 5 ( y + 3 )

⇒ 6x + 18 = 5y + 15------eq ( 2 ) ( say ).

By equating eq ( 1 ) and eq ( 2 ) , we get

11x + 22 = 6x + 18 and 9y + 18 = 5y + 15

⇒11x - 6x = 18 - 22 and 9y - 5y = 15 - 18

⇒5x = - 4 and 4y = - 3

⇒ x = - 4 / 5 and y = - 3 / 4

Hence , the fraction = x /y = ( - 4 / 5 ) / ( - 3 / 4 ) = ( - 4 / 5 ) × ( 4 / - 3 ) = 16 / 15.