Question

If 1 is added to each of numerator and denominator of a fraction, it becomes 2/3. However, if 1 is subtracted from each of numerator and denominator it becomes 3/5. Find the fraction

Answer 1

Hey friend..!! here's your answer
_________________________

Let the numerator = x
denominator = y

According to question,

x + 1 / y + 1 = 2 / 3

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

x - 1 / y - 1 = 3 / 5
5x - 5 = 3y - 3
5x - 3y =2 ------------------2

We get 2 question , Now by Elimination Method ,

3x - 2y = -1 × 5
5x - 3y = 2 × 3

15x - 10y = -5
15x - 9y = 6
- + -
__________
-y = -11

y = 11

Now put the value of in equation 1

3x - 2(11) = - 1
3x - 22 = -1
3x = 21
x = 7

So that the value of x is and y is 11.

We know numerator = x and denominator = y

Numerator / Denominator = 7 / 11

So that the fraction is 7 / 11

____________________
#Hope its help you dear#
☺

Answer 2

let numerator be x
denominator be y

(x + 1) / (y + 1) = 2 / 3

3x + 3 = 2y + 2

3x - 2y = -1 eq1

(x - 1) / (y - 1) = 3 /5

5x - 5 = 3y - 3

5x - 3y = 2 eq2

Now multiply eq1 by 5 and eq2 by 3 and subtract we get

15x + 10y = -5
-15x + 9y = -6

19x = -11

x = -11/19

put x= -11/19 in eq 1

3× -11/19 + 2y = -1

2y = -1 +33/19

2y = 14 / 19

y = 7 / 19

Fractions is x / y = (-11/19) /( 7/19)

= - 11 / 7

Thanks