Hello XxItzYourLifexX!
[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]
- Find the required fraction.
[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
Let's take the fraction as x/y , where x = numerator & y = denominator.
Given,
1st condition :-
[tex] \rightarrow \frac{x + 1}{y - 1} = 1 \: \: \: \: \: \: \: \: \: - - (1) \\ [/tex]
2nd condition :-
[tex] \rightarrow \frac{x}{y + 1} = \frac{1}{2}\: \: \: \: \: \: \: \: \: - - (2) \\ [/tex]
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Now, let's take eq. (2) & find the value of x using cross multiplication.
[tex] \frac{x}{y + 1} = \frac{1}{2} \\ 2x = 1(y + 1) \\ 2x = y + 1 \\ x = \frac{y + 1}{2} [/tex]
We got x as y+1/2. Now, let's substitute this value of x in eq. (1) & solve it using cross multiplication.
[tex] \frac{x + 1}{y - 1} = 1 \\ \frac{ \frac{y + 1}{2} + 1 }{y - 1} = 1 \\ \frac{ \frac{y + 1}{2} + 1}{y - 1} = \frac{1}{1} \\ \frac{y + 1}{2} + 1 = y - 1 \\ \frac{y + 3}{2} = y - 1 \\ y + 3 = 2(y - 1) \\ y + 3 = 2y - 2 \\ y - 2y = - 2 - 3 \\ - y = - 5 \\ \boxed{ y = 5}[/tex]
The value of y is 5. Now, let's find x. (x = y+1/2)
[tex]x = \frac{y + 1}{2} \\ x = \frac{5 + 1}{2} \\ x = \frac{6}{2} \\ \boxed{x = 3}[/tex]
So, the values of x & y respectively are 3 & 5. Now, the required fraction will come in the form of x/y. So, the fraction is...
[tex] \frac{x}{y} \\ = \large\boxed{\boxed{ \bf\frac{3}{5} }}[/tex]
- The correct answer is 3/5 (option b).
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Hope it'll help you!
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