Question

The denominator of a fraction is 4 more than the numerator. if both the numerator and the denominator are increased by 1, the resulting fraction equals 1/2. find the original fraction.

Answer 1

The original fraction is
`(3)/(7)` .

Explanation:

Given as :

Let The original fraction =
`(x)/(y)`

Where numerator = x

And denominator = y

The denominator of a fraction is 4 more than the numerator.

I.e y = x + 4

Or, y - x = 4 ........A

Again

If both the numerator and the denominator are increased by 1, the resulting fraction = 1/2

I.e
`(x + 1)/(y + 1)` =
`(1)/(2)`

using cross multiplication

2 × (x + 1) = 1 × (y + 1)

Or, 2 x + 2 = y + 1

Or, 2 x - y = 1 - 2

i.e 2 x - y = - 1 ..........B

Solving eq A and eq B

So, (2 x - y) + (y - x) = - 1 + 4

Or, (2 x - x) + ( - y + y) = 3

Or, x + 0 = 3

∴ x = 3

So, The numerator = x = 3

Now, put the value of x into eq A

∵ y - x = 4

Or, y - 3 = 4

Or, y = 4 + 3

∴ y = 7

So, The denominator = y = 7

So, The original fraction =
`(x)/(y)` =
`(3)/(7)`

Hence, The original fraction is
`(3)/(7)` . Answer