the sum of the numerator and denominator of a certain fraction is 8 .if 2 is added to the numerator and to the denominator, the value of the fraction is increased by 4/35.find fraction

This question can be solved by using both algebra and by choosing numbers. I just went ahead with the later one. So when p is 3 and q is 5 the sum will be 8. If we add 2 to both numerator and denominator, the new fraction becomes 5/7. By subtracting 3/5 from 5/7 we get 4/35.

How you choose 3 and 5 … it can be 2 and 6 etc

Cuz 2 and 6 doesnt work. You need to try various numbers.

Ok is there any shortcut to find perfect number or we have to try one by one

Let the numerator of the fraction be x. Then the denominator is 8 - x.

The question tells that if the numerator and denominator is increased by 2, we get the value increasing by 4/35. This means that

\frac{x + 2}{(8 - x) + 2} = \frac{x}{8 - x} + \frac{4}{35}

Solve for x.

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