Question

A fraction becomes 9/11,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

x+2/y+2=9/11
11x+22=9y+18
11x-9y=-4 equation (1)

x+3/y+3=5/6
6x+18=5y+15
6x-5y=-3equation (2)

by elimination method we find the value of x and y
multiply 1 equation by 5 =55x-45y=-20 equation 3
multiply 2 equation by 9 =54x-45y=-27 equation 4


now subtract equation4 from 3 equation

x=7
y=405/45
fraction=45×7/405=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.