Question

if 1 is added to numerator of a fraction the resulting fraction has a value 3 upon 4 on the other hand if 2 is added to denominator of that fraction the resulting fraction is of the value of one upon to find the original fraction​

Answer 1

Correct question:-

if 1 is added to numerator of a fraction the resulting fraction has a value 3/4. On the other hand if 2 is added to denominator of that fraction the resulting fraction is of the value of 1/2. Find the original fraction

Answer:-

Let the original fraction be x/y

For first case,

On adding 1 to the numerator of the original fraction, we get (x + 1)/y

And it is given that, it is equal to 3/4

So,

(x + 1)/y = 3/4

→ 4(x + 1) = 3y

→ 4x + 4 = 3y

→ 4x = 3y - 4 ----( 1 )

For second case,

On adding 2 to the denominator of the original fraction, we get x/(y + 2)

And it is given that, it is equal to 1/2

So,

x/(y + 2) = 1/2

→ 2x = y + 2

Multiplying both sides with 2,

→ 2 * 2x = 2 * (y + 2)

→ 4x = 2y + 4 ----( 2 )

But from ( 1 ),

4x = 3y - 4

So, from ( 1 ) and ( 2 ),

3y - 4 = 2y + 4

→ 3y - 2y = 4 + 4

→ y = 8

Putting the value of y in equation ( 1 ),

4x = 3y - 4

→ 4x = (3 * 8) - 4

→ 4x = 24 - 4

→ 4x = 20

→ x = 5

Hence,

the original fraction = x/y = 5/8 Ans.