Question

The sum of the numerator and denominator of a certain fraction is 10 if 1 is subtracted from both numerator and denominator the fraction is decrease by 2/21 find the fraction

Answer 1

take numerator as X and denominator as Y. use the given conditions in questions and use elimination method to solve the equation

Answer 2

Answer:

The Fraction are $\frac{-5}{15}\:\:or\:\:\frac{3}{7}$

Step-by-step explanation:

Given: Sum of numerator and denominator  10

To find: The fraction

let the numerator be x

So, the denominator = 10 - x

According to the question,

$\frac{x}{10-x}-\frac{x-1}{10-x-1}=\frac{2}{21}$

$\frac{x(9-x)-(x-1)(10-x)}{(10-x)(9-x)}=\frac{2}{21}$

$\frac{9x-x^2-(11x-10-x^2)}{90-19x+x^2}=\frac{2}{21}$

$\frac{9x-x^2-11x+10+x^2}{90-19x+x^2}=\frac{2}{21}$

$\frac{10-2x}{90-19x+x^2}=\frac{2}{21}$

$21(10-2x)=2(90-19x+x^2)$

$210-42x=180-38x+2x^2$

$30-4x-2x^2=0$

$x^2+2x-15=0$

on solving, we get

x = -5 and 3

when x = -5

the fraction = $\frac{-5}{10-(-5)}=\frac{-5}{15}$

when x = 3

the fraction = $\frac{3}{10-(3)}=\frac{3}{7}$

Therefore, The Fraction are $\frac{-5}{15}\:\:or\:\:\frac{3}{7}$