Question

The numerator of a fraction is 3 less than the denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and the original fraction is $\frac{29}{20}$. Find the original fraction.

Answer 1

SOLUTION :  

Let x be the denominator of a original fraction.

Then, Numerator be  (x - 3)

Original Fraction = Numerator/ denominator = (x - 3)/x

New  fraction = (x - 3 + 2)/(x + 2) = (x - 1)/(x + 2)

[When 2 is added to numerator and denominator]

New  fraction = (x - 1)/(x + 2)

A.T.Q  

(x - 3)/x + (x - 1)/(x + 2) = 29/20

[ (x - 3)(x + 2) + x(x -1)] / x(x + 2) = 29/20

[By taking LCM]

[(x² - 6 - x + x² - x)] / x² + 2x = 29/20

20(2x² - 2x - 6) = 29(x² + 2x)

[By cross multiplication]

40x² - 120 - 40x = 29x² + 58x  

40x² - 29x² - 40x - 58x - 120 = 0

11x² - 98x - 120 = 0

11x² - 110x + 12x -120 = 0

[By middle term splitting]

(11x + 12)(x - 10) = 0

(11x + 12)  = 0  or (x - 10) = 0

11x = - 12  or x = 10  

x = -12/11 or x = 10  

Since, x is a natural number , so x ≠ - 12/11

Therefore, x = 10

Numerator = (x - 3) = 10 - 3 = 7/10

Original Fraction = (x - 3)/x = (10 - 3)/10 = 7/10

Hence, the original fraction is 7/10.

HOPE THIS  ANSWER WILL HELP YOU..

Answer 2

here is your answer, hope this helps