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 â€˜xâ€™

So the numerator will be â€˜8-xâ€™

The obtained fraction is (8-x)/x

So according to the question,

By cross multiplying,

35(4x â€“ 16) = 4(x

^{2Â }+ 2x)140x â€“ 560 = 4x

^{2}Â + 8x4x

^{2}Â + 8x â€“ 140x + 560 = 04x

^{2}Â â€“ 132x + 560 = 0Divide by 4, we get

x

^{2}Â â€“ 33x + 140 = 0let us factorize,

x

^{2}Â â€“ 28x â€“ 5x + 140 = 0x(x â€“ 28) â€“ 5 (x â€“ 28) = 0

(x â€“ 28) (x â€“ 5) = 0

So,

(x â€“ 28) = 0 or (x â€“ 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 â€“ 5)/5 = 3/5

âˆ´ The required fraction is = 3/5