Question

In a fraction twice the numerator is 2 more than the denominator. If 3 is added to the numerator and to the denominator the new fraction is 2/3. the original fraction is.​

Answer 1

Let the fraction be x/y

where x is numerator and y is denominator

According to 1 st condition

2x=2 + y

2x-y=2

4x-2y=4...(1)

According to 2nd condition

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

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

3x+9=2y+6

3x-2y=6-9

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

subtracting equation (2) from (1)

4x-2y=4

3x-2y=-3

_________

x=7

substituting x=7 in equation 2

3×7 -2y=-3

21-2y=-3

-2y=-3-21

-2y=-24

y=12

Therefore the fraction x/y=7/12

Hope it helps you..☺☺

Answer 2

Answer:

Step-by-step explanation:

Let numerator be x and denominator be y.

Acc. to the question,

2x=y+2

2x-y=2.....eq.1

After adding 3 to numerator and denominator

x+3/y+3=2/3

On cross multiplying

3x+9=2y+6

2y-3x =3......eq.2

On simultaneously solving the 2 equations,

x=7 and y=12.

So the original fraction is 7/12