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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

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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,

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1. 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(x2Â + 2x)

140x â€“ 560 = 4x2Â + 8x

4x2Â + 8x â€“ 140x + 560 = 0

4x2Â â€“ 132x + 560 = 0

Divide by 4, we get

x2Â â€“ 33x + 140 = 0

let us factorize,

x2Â â€“ 28x â€“ 5x + 140 = 0

x(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

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