Answer
455.1k+ views
Hint: First make linear equations from the given information and then solve those equations in order to find the value of two numbers.
Let the numerator be $x$and denominator be$y$.
According to the question:
\[
{\text{Case1: }}x = y - 4{\text{ }} \ldots \ldots \left( 1 \right) \\
{\text{Case2: }}8\left( {x - 2} \right) = y + 1 \\
\Rightarrow 8x - 16 = y + 1 \\
\Rightarrow 8x - y = 17{\text{ }} \ldots \ldots \left( 2 \right) \\
\]
Put the value of $x$from equation $\left( 1 \right)$in equation $\left( 2 \right)$and solve for$y$, we get:
\[
\Rightarrow 8\left( {y - 4} \right) - y = 17 \\
\Rightarrow 8y - 32 - y = 17 \\
\Rightarrow 7y = 49 \\
\Rightarrow y = 7 \\
\]
Now, put the value of$y$in equation$\left( 1 \right)$and solve for$x$, we get:
\[
\Rightarrow x = y - 4 \\
\Rightarrow x = 7 - 4 \\
\Rightarrow x = 3 \\
\]
Hence, the fraction \[\dfrac{x}{y}\]is equal to \[\dfrac{3}{7}.\]
Now, the given fraction is of the form $\dfrac{m}{{14}}$. So, we will also convert our fraction of the same form.
Therefore, multiplying and dividing the fraction by\[2\], we get:
\[
\dfrac{x}{y}{\text{ = }}\dfrac{3}{7} \times \dfrac{2}{2} \\
\dfrac{x}{y} = \dfrac{6}{{14}}{\text{ }} \ldots \ldots \left( 3 \right) \\
\]
Now, the equation$\left( 3 \right)$is of the form $\dfrac{m}{{14}}$. By comparison, we get:
\[m = 6\]
Note- Whenever you see a problem like this, always try to identify the number of variables and try to make that many equations. Also, in order to compare two fractions, always make their denominator or numerator equal.
Let the numerator be $x$and denominator be$y$.
According to the question:
\[
{\text{Case1: }}x = y - 4{\text{ }} \ldots \ldots \left( 1 \right) \\
{\text{Case2: }}8\left( {x - 2} \right) = y + 1 \\
\Rightarrow 8x - 16 = y + 1 \\
\Rightarrow 8x - y = 17{\text{ }} \ldots \ldots \left( 2 \right) \\
\]
Put the value of $x$from equation $\left( 1 \right)$in equation $\left( 2 \right)$and solve for$y$, we get:
\[
\Rightarrow 8\left( {y - 4} \right) - y = 17 \\
\Rightarrow 8y - 32 - y = 17 \\
\Rightarrow 7y = 49 \\
\Rightarrow y = 7 \\
\]
Now, put the value of$y$in equation$\left( 1 \right)$and solve for$x$, we get:
\[
\Rightarrow x = y - 4 \\
\Rightarrow x = 7 - 4 \\
\Rightarrow x = 3 \\
\]
Hence, the fraction \[\dfrac{x}{y}\]is equal to \[\dfrac{3}{7}.\]
Now, the given fraction is of the form $\dfrac{m}{{14}}$. So, we will also convert our fraction of the same form.
Therefore, multiplying and dividing the fraction by\[2\], we get:
\[
\dfrac{x}{y}{\text{ = }}\dfrac{3}{7} \times \dfrac{2}{2} \\
\dfrac{x}{y} = \dfrac{6}{{14}}{\text{ }} \ldots \ldots \left( 3 \right) \\
\]
Now, the equation$\left( 3 \right)$is of the form $\dfrac{m}{{14}}$. By comparison, we get:
\[m = 6\]
Note- Whenever you see a problem like this, always try to identify the number of variables and try to make that many equations. Also, in order to compare two fractions, always make their denominator or numerator equal.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)