Question

A fraction becomes 2/3 when 1 ls added to both the numerator and denominator. And it becomes 1/2 when 1
subtracted from both the numerator and
denominator Find the fraction.

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Answer 1

Solution -

Let us assume, x be the numerator and y be the denominator of a fraction.

Therefore, given fraction is x/y

Given:

(x-1) / (y-1) = 1/3

3x - 3 = y - 1

3x - y = 2

y = 3x - 2 -------------------1

Also given:

(x+1) / (y+1) = 1/2

2x + 2 = y + 1

y - 2x = 1 -------------2

Substitute the value of y from equation 1

3x - 2 - 2x = 1

x - 2 = 1

x = 1 + 2

x = 3

Therefore, y = 3x - 2 = 3 * 3 - 2 = 7

y = 7

Therefore, the given fraction is x/y = 3/7

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Answer 2

Let the numerator be x and denomiantor be y.

Then, (x+1) / (y+1) = 2/3 (given)

So, 3x +3 = 2y +2

     3x- 2y = 2–3 = -1

     3x - 2y = -1     ......................(1)

(x-1) / (y-1) = 1/2 (given)  

So, 2x-2 = y-1

     2x - y = -1 + 2 = 1

     2x- y = 1       ......................(2)

(2)×2,

    4x - 2y = 2      .......................(3)

Subtracting EQ. 1 from EQ. 3, we get:

             x=3

Substituting the value of x in EQ.1, we get:

9- 2y = -1

2y = 10,

y = 5.

So, the original fraction is 3/5.

HOPE IT HELPS U............