Question

please solve please ​

Answer 1

Answer:

Let the numerator of the fraction be x and the denominator of the fraction be y, so that the fraction will be x/y.

Now, according to the question;

If 3 is added to the numerator of the fraction, it becomes 5/6.

=> (x+3)/y = 5/6

=> 6(x+3) = 5y

=> 6x + 18 = 5y

=> 6x - 5y + 18 = 0 ---------(1)

Also, If 5 is added to the numerator and 4 to the denominator, the fraction becomes 3/4.

=> (x+5)/(y+4) = 3/4

=> 4(x+5) = 3(y+4)

=> 4x + 20 = 3y + 12

=> 4x - 3y + 20 - 12 = 0

=> 4x - 3y + 8 = 0 ----------(2)

Multiplying the eq-(1) by 2 , we get;

12x - 10y + 36 = 0 -------------(3)

Multiplying the eq-(2) by 3 , we get;

12x - 9y + 24 = 0 -------------(4)

Now, subtracting eq-(4) from eq-(3)

We get;

=> (12x -10y + 36) - (12x - 9y + 24) = 0

=> 12x -10y + 36 - 12x + 9y - 24 = 0

=> -y + 12 = 0

=> y = 12

Now, putting the value y = 12 in eq-(2),

We get;

=> 4x - 3y + 8 = 0

=> 4x - 3(12) + 8 = 0

=> 4x - 36 + 8 = 0

=> 4x - 28 = 0

=> 4x = 28

=> x = 28/4

=> x = 7

Hence, the required fraction is x/y.

ie, 7/12.