Question

A fraction becomes 9 11 ⁄ if 2 is added to both the numerator and the  denominator, if 3 is added to both the numerator and denominator it  becomes 5 6 ⁄ .Find the fraction?​

Answer 1

Correct 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 ?

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 :-

• Fraction = ?

Solution :-

๏ Let Numerator be x and Denominator be y.

๏ Therefore, required fraction will be = Numerator ÷ Denominator = x ÷ y

★ According to Question :-

➝ (x + 2)/(y + 2) = 9/11

By cross multiplying both sides we get :

➝ 11(x + 2) = 9(y + 2)

➝ 11x + 22 = 9y + 18

➝ 22 - 18 = 9y - 11x

➝ 9y - 11x = 4

➝ 11x = 9y - 4

➝ x = 9y - 4 ÷ 11 ......[Equation (i)]

Then,

➝ (x + 3)/(y + 3) = 5/6

By cross multiplying both sides we get :

➝ 6(x + 3) = 5(y + 3)

➝ 6x + 18 = 5y + 15

➝ 6x + 18 - 5y - 15 = 0

➝ 6x - 5y + 3 = 0

Substituting value of x from equation (i) we get :

➝ 6(9y - 4)/11 - 5y + 3 = 0

➝ 54y - 24/11 = 5y - 3

➝ 54y - 24 = 11(5y - 3)

➝ 54y - 24 = 55y - 33

Combining like terms on both sides :

➝ -24 + 33 = 55y - 54y

➝ 55y - 54y = -24 + 33

➝ y = 9

Now, Substituting the value of 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

Hence,

• Numerator = x = 7
• Denomintaor = y = 9
• Required fraction = x/y = 7/9