Question

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

Answer 1

let the fraction
$x \div y$
Case 1.
$x + y = 10$
Case 2
$x - 1 \div y - 1 = 2 \div 21$
now solve the equation by any of three method

Answer 2

Answer:

The fraction is $\frac{3}{7}$

Step-by-step explanation:

Let x be the numerator of the fraction

⇒ denominator = 10-x

According to the question,

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

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

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

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

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

on solving this quadratic equation we get,

x = -5 and 3

faction does not have negative numerator

Numerator, x = 3  and denominator = 10 - x = 7

Therefore, The fraction is $\frac{3}{7}$