Answer
454.2k+ views
Hint- In order to solve such a question with multiple lines of cases consider the numerator and the denominator of the fraction in terms of some unknown variables and then try to make an algebraic equation with the help of given cases in question.
Let $a$ be the numerator of the fraction and $b$ be the denominator of the given fraction.
So the fraction becomes $\dfrac{a}{b}$
According to the first statement of the problem:
If we add 1 to the numerator and subtract 1 from the denominator a fraction reduces to 1
$
\Rightarrow \dfrac{{a + 1}}{{b - 1}} = 1 \\
\Rightarrow a + 1 = b - 1 \\
\Rightarrow a + 2 = b \\
\Rightarrow b = a + 2.............(1) \\
$
According to the second statement:
If we only add 1 to the denominators, it becomes $\dfrac{1}{2}$.
$
\Rightarrow \dfrac{a}{{b + 1}} = \dfrac{1}{2} \\
\Rightarrow 2a = b + 1 \\
\Rightarrow 2a - 1 = b \\
\Rightarrow b = 2a - 1..............(2) \\
$
From equations (1) and (2), equating the value of $b$ in both the cases.
$
\Rightarrow 2a - 1 = a + 2 \\
\Rightarrow 2a - a = 2 + 1 \\
\Rightarrow a = 3 \\
$
Now substituting the value of $a$ in equation (1)
$
\Rightarrow b = 3 + 2 \\
\Rightarrow b = 5 \\
$
Finally the fraction $\dfrac{a}{b} = \dfrac{3}{5}$ .
Hence, the fraction is $\dfrac{3}{5}$ .
Note- We know that fraction is defined as the ratio of numerator and denominator. In order to solve such questions algebraic method is the only way to proceed for an easy and fast solution. It consists of considering the numerator and denominator in terms of some unknown variables and then satisfying the given conditions on the basis of variables to find the equation.
Let $a$ be the numerator of the fraction and $b$ be the denominator of the given fraction.
So the fraction becomes $\dfrac{a}{b}$
According to the first statement of the problem:
If we add 1 to the numerator and subtract 1 from the denominator a fraction reduces to 1
$
\Rightarrow \dfrac{{a + 1}}{{b - 1}} = 1 \\
\Rightarrow a + 1 = b - 1 \\
\Rightarrow a + 2 = b \\
\Rightarrow b = a + 2.............(1) \\
$
According to the second statement:
If we only add 1 to the denominators, it becomes $\dfrac{1}{2}$.
$
\Rightarrow \dfrac{a}{{b + 1}} = \dfrac{1}{2} \\
\Rightarrow 2a = b + 1 \\
\Rightarrow 2a - 1 = b \\
\Rightarrow b = 2a - 1..............(2) \\
$
From equations (1) and (2), equating the value of $b$ in both the cases.
$
\Rightarrow 2a - 1 = a + 2 \\
\Rightarrow 2a - a = 2 + 1 \\
\Rightarrow a = 3 \\
$
Now substituting the value of $a$ in equation (1)
$
\Rightarrow b = 3 + 2 \\
\Rightarrow b = 5 \\
$
Finally the fraction $\dfrac{a}{b} = \dfrac{3}{5}$ .
Hence, the fraction is $\dfrac{3}{5}$ .
Note- We know that fraction is defined as the ratio of numerator and denominator. In order to solve such questions algebraic method is the only way to proceed for an easy and fast solution. It consists of considering the numerator and denominator in terms of some unknown variables and then satisfying the given conditions on the basis of variables to find the equation.
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)