Question

question..........

The denominator of a fraction is 1 more than Thrice its numerator. if the numerator is increased
by 1 and denominator is decreased by 1 then the number obtained is 1/2 Find the fraction.

Answer 1

Answer:

The Fraction is $\boxed{\boxed{\tt{\frac{2}{7}}}}$

Step-by-step explanation:

Given :

• Denominator of the Fraction = 1 more than thrice its numerator
• When Numerator is increased by 1 and Denominator is decreased by 1 then the number obtained is $\dfrac{1}{2}$

To Find :

• The fraction

Solution :

✯ $\textbf{\small{\underline{Consider the -}}}$

• Numerator as x
• Denominator as (3x + 1)

Original Fraction = $\dfrac{x}{(3x+1)}$

$\rule{300}{1.5}$

✯ $\textbf{\small{\underline{According to the Question -}}}$

When Numerator is increased by 1 and Denominator is decreased by 1 then the number obtained is $\dfrac{1}{2}$

★ $\boxed{\tt{\frac{x + 1}{(3x + 1) - 1} = \frac{1}{2}}}$

$\tt{\longrightarrow} \: \dfrac{x + 1}{(3x + 1) - 1} = \dfrac{1}{2}$

$\tt{\longrightarrow} \: \dfrac{x + 1}{3x} = \dfrac{1}{2}$

$\tt{\longrightarrow} \:2(x + 1) = 1(3x)$

$\tt{\longrightarrow} \:2x + 2= 3x$

$\tt{\longrightarrow} \:3x - 2x =2$

$\tt{\longrightarrow} \:x =2$

Numerator = 2

$\rule{300}{1.5}$

★ Value of (3x + 1)

$\tt{\longrightarrow} \:3(2) + 1$

$\tt{\longrightarrow} \:6 + 1$

$\tt{\longrightarrow} \:7$

Denominator = 7

• Numerator = 2
• Denominator = 7

Fraction is = $\boxed{\boxed{\tt{\frac{2}{7}}}}$

$\therefore$ The Fraction $\dfrac{2}{7}$

Answer 2

Answer:

The Fraction is $\dfrac{2}{7}$

Step-by-step explanation:

Let the Numerator be as x

The denominator of the fraction is one more than thrice the numerator. So, the denominator is 3x + 1

Thus the Fraction is $\dfrac{y}{3y+ 1}$

As the number obtained when the numerator is increased by 1 and denominator is decreased by 1 is $\dfrac{1}{2}$, We have =

$\bf{\implies}\: \dfrac{(y) + 1}{(3y + 1) - 1} = \dfrac{1}{2}$

$\bf{\implies}\: \dfrac{y+ 1}{3y } = \dfrac{1}{2}$

$\bf{\implies}\: Cross \: multiply$

$\bf{\implies}\: 2(y + 1) = 1(3y)$

$\bf{\implies}\: 2y + 2 = 3y$

$\bf{\implies}\: 2y - 3y = - 2$

$\bf{\implies}\: \cancel - y = \cancel - 2$

$\bf{\implies}\: Numerator = 2$

Denominator =

$\bf{\implies}\: 3y + 1$

$\bf{\implies}\: 3(2) + 1$

$\bf{\implies}\: 7$

$\bf{\implies}\: Denominator = 7$

Fraction = $\dfrac{2}{7}$

$\therefore$ The Fraction is $\dfrac{2}{7}$