Question

The sum of the numerator and
denominator of a is greater by 1 than thrice the numerator If the numerator is decreased by 1 then the fraction reduces to 1/3 ..
find the fraction.​

Answer 1

GIVEN:

• The sum of the numerator and
• denominator of a fraction is greater by 1 than thrice the numerator.
• If the numerator is decreased by 1 then the fraction reduces to 1/3

TO FIND:

• What is the fraction ?

SOLUTION:

Let the numerator of the fraction be 'x' and the denominator of the fraction be 'y'.

So, the fraction will become

$\bf{\star \: Fraction = \dfrac{Numerator}{Denominator} = \dfrac{x}{y}}$

CASE:- 1

The sum of the numerator and denominator of a fraction is greater by 1 than thrice the numerator.

$\rm{\hookrightarrow x + y = 3x + 1 }$

$\rm{\hookrightarrow -1 = 3x - x -y }$

$\bf{\hookrightarrow -1 = 2x - y...1) }$

$\rm{\hookrightarrow y = 2x + 1}$

CASE:- 2

If the numerator is decreased by 1 then the fraction reduces to 1/3.

$\rm{\hookrightarrow \dfrac{x - 1}{y} = \dfrac{1}{3} }$

$\rm{\hookrightarrow 3(x-1) = y }$

$\rm{\hookrightarrow 3x - 3 = y }$

$\bf{\hookrightarrow 3x - y = 3...2) }$

Put the value of 'y' from equation 1) in equation 2)

$\rm{\hookrightarrow 3x -(2x+1) = 3}$

$\rm{\hookrightarrow 3x - 2x - 1 = 3}$

$\rm{\hookrightarrow 3x - 2x = 3 + 1 }$

$\bf{\hookrightarrow x = 4 }$

Put the value of 'x' in equation 1)

$\rm{\hookrightarrow 2 \times 4 - y = -1 }$

$\rm{\hookrightarrow 8 - y = -1}$

$\rm{\hookrightarrow -y = -1 -8 }$

$\bf{\hookrightarrow y = 9 }$

• FRACTION = x/y
• FRACTION = 4/9

______________________

Answer 2

the answer is in the picture..