Question

If the numerator of a fraction is multiplied by 2 and its denominator is increased by 2, it becomes 6/7. If instead we multiply the denominator by 2 and increase the numerator by 2 it reduces to 1/2. What is the fraction?

Answer 1

Let the fraction be $\frac {x} {y}$

Case I,

$\frac {2x} {y+2}$ = $\frac {6} {7}$

Cross multiply

14x = 6y +12. ... (1)
14x-6y = 12

Case II,

$\frac {x+2} {2y}$ = $\frac {1} {2}$

Cross Multiplication

2x+4 = 2y
2x-2y = -4
x -y = -2

Multiply by 6

6x-6y = -12. ....(2)

From 1 and 2, (subtract)

8x = 24

x= 3

Put in eq
3-y= -2
y = 5

So the fraction is $\frac {3} {5}$

Answer 2

Hope it helps u.. ....