Question

the denominator of a fraction is 5 more than the numerator. increasing the numberator and denominator by 3,we get the fraction 1/2 find the fraction​

Answer 1

$\huge\color{aqua}answer : -$

$- - >\huge \frac{2}{7}$

$\huge \color{violet}explanation : -$

☆To find :-

• The original fraction

☆Given:-

• The denominator of the fraction is 5 more than the numerator.

• Increasing the numerator and denominator by 3 ,the fraction becomes 1/2

☆Assuming:-

• Let the numerator be x

• Therefore, denominator = x+5

☆Solution:-

• Therefore, the fraction

$- > \frac{x }{x + 5}$

• When increased the numerator and denominator by 3 ,the fraction:

$- > \frac{x + 3}{x + 5 + 3} = \frac{x + 3}{x + 8}$

ATQ

$\frac{x + 3}{x + 8} = \frac{1}{2} \\ = > 2(x + 3) = x + 8 \\ = > 2x + 6 = x + 8 \\ = > 2x - x = 8 - 6 \\ = > x = 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Therefore the numerator = x= 2
• And denominator = x+5 =2+5=7

☆Hence :-

• The fraction is

$- > \frac{2}{7}$

Verification:-

$\frac{2 + 3}{7 + 3} = \frac{5}{10} = \frac{1}{2}$

Hence proved

hope it helps .... :)