Question

The numerator of a fraction is four
less than its denominator. If 1 is
added to both numerator and
denominator, the fraction becomes
1/2.Find the fraction. *
O 3/6
O 2/7
3/7
O 1/7​

Answer 1

Answer :-

$\implies \cfrac {3}{7}$

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Equation :-

$\implies \cfrac{x - 4 + 1}{x + 1} = \cfrac{1}{2}$

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Given :-

• Numerator of Fraction is 4 less than it's denominator.

• If 1 is added to both numerator and denominator the fraction becomes 1/2.

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Step By Step Solution :-

This is a Question from Linear Equations for one variable. So Let's do it !!

$\implies\cfrac{x - 4 + 1}{x + 1} = \cfrac{1}{2} \\ \\ \implies \cfrac{x - 3}{x + 1} = \cfrac{1}{2} \\ \\ \implies \:2 \times ( x - 3) = 1 \times (x + 1) \\ \\ \implies \: 2x - 6 = x + 1 \\ \\ \implies \: 2x - x = 1 + 6 \\ \\ \implies \: x = 7$

Now Fraction ⤵

$\cfrac{x - 4}{x} \implies \cfrac{7 - 4}{7} \\ \\ \implies\cfrac{3}{7}$

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Verification :-

By Putting the value of X

• L. H. S. ⤵

$\implies\cfrac{7 - 4 + 1}{7 + 1} \\ \\ \implies \cfrac{3 + 1}{8} \\ \\ \implies \cfrac { \cancel4}{ \cancel8} \\ \\ \implies \cfrac{1}{2}$

• R. H. S. ⤵

$\implies \cfrac{1}{2}$

Therefore L. H. S. = R. H. S.

Hence Proved .

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