Question

The Denominator of a fractions is greater than its numerator by 12. if the numerator is decreased by 2 & the denominator is increased by 7, the new fraction is equivalent with 1/2. find the fraction.
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Answer 1

Question -

The Denominator of a fractions is greater than its numerator by 12. If the numerator is decreased by 2 & the denominator is increased by 7, the new fraction is equivalent with ${\frac{1}{2}}$. Find the fraction.

Solution -

${\sf{Let \ numerator \ be \ x \ .}}$

${\sf{Denominator \ is \ 12 \ more \ than \ numerator = 12+x}}$

${\sf{\large{\therefore \ Fraction \ = \ \frac{x}{12}}}}$

Now, According to question

${\sf{✿ \ If \ the \ numerator \ is \ decreased \ by \ 2 \ and \ the }}\\{\sf{ denominator \ is \ increased \ by \ 7, \ then \ the }}\\{\sf{ fraction \ will \ be\ \frac{1}{2}}}$

${\sf{\leadsto \ \frac{x - 2}{x + 12 + 7} = \frac{1}{2} }}$

${\sf{\leadsto \ \frac{x - 2}{x + 18} = \frac{1}{2} }}$

Cross multiplying

${\sf{\leadsto \ 2x - 4 = x + 18}}$

${\sf{\leadsto \ 2x-x = 18+4}}$

${\sf{\leadsto \ x = 22}}$

Now,

${\sf{✯ \ Fraction \ = \ \frac{x}{x+12} \implies \ \frac{22}{34}}}$

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Answer 2

Answer:

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