Question

If the numerator of a fraction is decreased by 2 and the denominator is increased by 1, the new fraction is 3 4 . If the numerator of a fraction is increased by 2 and the denominator is decreased by 1, the new fraction is 7 2 . The fraction =

Answer 1

Answer:

Let the fraction be

y

x

As per the given statements,

y−4

x+2

=2

⇒x+2=2y−8

⇒x−2y=−10 --- (1)

Also,

y+2

x−1

=

3

1

⇒3x−3=y+2

⇒3x−y=5 --- (2)

Multiplying eqn (2) by 2 and subtracting eqn (1) from it, we get

2(3x−y)−(x−2y)=2(5)−(−10)

⇒5x=20

⇒x=4

Substituting this value of x in eqn (2), we get

3(4)−y=5

⇒y=12−5=7

∴x=4;y=7

So, x+y=4+7=11