Question

1 The denominator of a rational number is greater than its numerator by 7. If the numerator
is increased by 17 and the denominator decreased by 6, the new number becomes 2. Find
the original number.
is added to the​

Answer 1

Answer:

Appropriate Question :-

• The denominator of a rational number is greater than its numerator by 7. If the numerator is increased by 17 and the denominator decreased by 6, the new number becomes 2. Find the original fraction.

Given :-

• The denominator of a rational number is greater than its numerator by 7.
• The numerator is increased by 17 and the denominator decreased by 6.
• The new numbers becomes 2.

To Find :-

• What is the original fraction.

Solution :-

Let,

$\mapsto \bf{Numerator =\: x}$

$\mapsto \bf{Denominator =\: x + 7}$

Hence, the required original fraction is :

$\leadsto \sf \dfrac{Numerator}{Denominator}$

$\leadsto \sf \bold{\green{\dfrac{x}{x + 7}}}$

According to the question,

$\implies \sf \dfrac{x + 17}{x + 7 - 6} =\: 2$

$\implies \sf \dfrac{x + 17}{x + 1} =\: 2$

By doing cross multiplication we get,

$\implies \sf 2(x + 1) =\: x + 17$

$\implies \sf 2x + 2 =\: x + 17$

$\implies \sf 2x - x =\: 17 - 2$

$\implies \sf\bold{\purple{x =\: 15}}$

Hence, the required original fraction will be :

$\longrightarrow \sf Original\: fraction =\: \dfrac{x}{x + 7}$

$\longrightarrow \sf Original\: fraction =\: \dfrac{15}{15 + 7}$

$\longrightarrow \sf\bold{\red{Original\: fraction =\: \dfrac{15}{22}}}$

${\small{\bold{\underline{\therefore\: The\: original\: fraction\: is\: \dfrac{15}{22}\: .}}}}$

Answer 2

Answer:

Appropriate Question :-

The denominator of a rational number is greater than its numerator by 7. If the numerator is increased by 17 and the denominator decreased by 6, the new number becomes 2. Find the original fraction.

Given :-

The denominator of a rational number is greater than its numerator by 7.

The numerator is increased by 17 and the denominator decreased by 6.

The new numbers becomes 2.

To Find :-

What is the original fraction.

Solution :-

Let,

\mapsto \bf{Numerator =\: x}↦Numerator=x

\mapsto \bf{Denominator =\: x + 7}↦Denominator=x+7

Hence, the required original fraction is :

\leadsto \sf \dfrac{Numerator}{Denominator}⇝DenominatorNumerator

\leadsto \sf \bold{\green{\dfrac{x}{x + 7}}}⇝x+7x

According to the question,

\implies \sf \dfrac{x + 17}{x + 7 - 6} =\: 2⟹x+7−6x+17=2

\implies \sf \dfrac{x + 17}{x + 1} =\: 2⟹x+1x+17=2

By doing cross multiplication we get,

\implies \sf 2(x + 1) =\: x + 17⟹2(x+1)=x+17

\implies \sf 2x + 2 =\: x + 17⟹2x+2=x+17

\implies \sf 2x - x =\: 17 - 2⟹2x−x=17−2

\implies \sf\bold{\purple{x =\: 15}}⟹x=15

Hence, the required original fraction will be :

\longrightarrow \sf Original\: fraction =\: \dfrac{x}{x + 7}⟶Originalfraction=x+7x

\longrightarrow \sf Original\: fraction =\: \dfrac{15}{15 + 7}⟶Originalfraction=15+715

\begin{gathered}\longrightarrow \sf\bold{\red{Original\: fraction =\: \dfrac{15}{22}}}\\\end{gathered}⟶Originalfraction=2215

\begin{gathered}{\small{\bold{\underline{\therefore\: The\: original\: fraction\: is\: \dfrac{15}{22}\: .}}}}\\\end{gathered}∴Theoriginalfractionis2215.