Question

If 1 is added to both the numerator and denominator of a fraction in because 4 by 5 if 5 is subtracted from both the numerator and denominator the fraction becomes 1 by 2 find the fraction

Answer 1

Answer:

Let the fraction be = $\tt {\frac {x}{y}}$

According to question:

$\tt {\frac {x+1}{y+1} = \frac {4}{5}}$

=> 5x + 5 = 4y + 4

=> x = (4y - 1)/5

Next equation:

$\tt {\frac {x-5}{y-5} = \frac {1}{2}}$

=> 2x - 10 = y - 5

=> x = (y + 5)/2

● (4y - 1)/5 = (y + 5)/2

8y - 2 = 5y + 25

3y = 27

y = 9

● x = (4y - 1)/5

(36 - 1)/5

x = 7