This question has been taken from Book:- ML aggarwal, Avichal publication, class10th, quadratic equation in one variable, chapter 5, exercise 5.5
This is an important ques and asked in exam
The sum of the numerator and denominator of a certain positive fraction is 8.
If 2 is added to both the numerator and denominator,
the fraction is increased by 4/35. Find the fraction
Question no10. ,ML Aggarwal, chapter 5, exercise 5.5, quadratic equation in one variable, ICSE board,
Solution:
Let the denominator be ‘x’
So the numerator will be ‘8-x’
The obtained fraction is (8-x)/x
So according to the question,
By cross multiplying,
35(4x – 16) = 4(x2 + 2x)
140x – 560 = 4x2 + 8x
4x2 + 8x – 140x + 560 = 0
4x2 – 132x + 560 = 0
Divide by 4, we get
x2 – 33x + 140 = 0
let us factorize,
x2 – 28x – 5x + 140 = 0
x(x – 28) – 5 (x – 28) = 0
(x – 28) (x – 5) = 0
So,
(x – 28) = 0 or (x – 5) = 0
x = 28 or x = 5
So the value of x = 5 [since, x = 28 is not possible as sum of numerator and denominator is 8]
When substitute the value of x = 5 in the fraction (8-x)/x, we get
(8 – 5)/5 = 3/5
∴ The required fraction is = 3/5