Question

1. When 2 is added to the denominator and 3 is subtracted from the numerator a fraction becomes
2/9.and when
when 7 added to numerator and the denominator is multiplied by 3 it becomes 4/7.
find fraction
​

Answer 1

let the numerator and denominator be x and y .

x-3/y+2=2/9....(1)

crossmultiply it

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

9x-27=2y+4

9x-2y-27-4=0

9x-2y-31=0

9x-2y=31.......(2)

x+7/3y=4/7.....(3)

crossmultiply it

4(x+7)=7(3y)

4x+28=21y

4x-21y=-28....(4)

by elemination method

multiply equation (2) with 4 and equation(4)with 9

subtract both the equations

36x-8y=124

-(36x-189y=-252)

36x-8y=124

-36x+189y=252

0 +181y=376

y= 376

181

y=2

putting the value of y in equation (2)

9x-2(4)=31

9x-4=31

9x=31+4

x=35

9

x=3

hope it will help you

Answer 2

Let the numerator be x and denominator be y

⇒Nowbyfirstcondition

y+3

x−2

=

4

1

.

⇒4(x−2)=(y+3)

⇒4x−8=y+3=>4x−y=11........................1

And By second condition

3y

x+6

=

3

2

⇒3(x+6)=6y

⇒3x−6y=−18............................................2

6(1)−(2)

21x=84

x=4

by1y=5