Question

A fraction becomes 9/11, if 2 added to both numerator and denominator. 3 is added to both numerator and denominator it becomes 5/6. find fraction.
With cross multiplication method


Please answer me ​

Answer 1

X+2/Y+2 = 9/11

11x+22=9y+18

11x-9y= 18-22

11x-9y= -4------------(1)

X+3/Y+3= 5/6

6x+18= 5y+15

6x-5y= 15-18

6x-5y= -3-------------(2)

This question is ❌wrong not cross multiplication method.

This question is solve by Substitution method.

Answer 2

Answer:-

Let the fraction be x/y.

Given:

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

→ (x + 2)/(y + 2) = 9/11

→ 11(x + 2) = 9(y + 2)

→ 11x + 22 = 9y + 18

→ 11x = 9y + 18 - 22

→ 11x = 9y - 4

$\sf \longrightarrow\: x = \dfrac{9y - 4}{11} \: \: -- \: \: equation \: (1).$

And,

It becomes 5/6 if 3 is added to both numerator and denominator.

→ (x + 3)/(y + 3) = 5/6

→ 6(x + 3) = 5(y + 3)

→ 6x + 18 = 5y + 15

Substitute the value of x from equation (1).

$\sf \: \longrightarrow \: 6 \bigg( \dfrac{9y - 4}{11} \bigg) + 18 = 5y + 15 \\ \\ \sf \: \longrightarrow \: \frac{54y - 24 + 11 \times18}{11} = 5y + 15 \\ \\ \sf\longrightarrow \: 54y - 24 + 198 = 11(5y + 15)$

→ 54y + 174 = 55y + 165

→ 174 - 165 = 55y - 54y

→ 9 = y

Putting the value of y in equation (1) we get,

$\sf\longrightarrow \: x = \frac{9 \times 9 - 4}{11} \\ \\ \sf\longrightarrow \: x = \frac{81 - 4}{11}$

→ x = 77/11

→ x = 7

Hence, the required fraction x/y is 7/9.