Math, asked by shrutikataria106, 11 months ago

The numerator of a fraction is less than the denominatior by 2. If 3 is added to both, the numerator and the denominator, the fraction becomes 4/5. Find the original fraction.

Answers

Answered by kiki9876
6

Let the denominator be x

Numerator= x-2

Fraction=

 \frac{x - 2}{x}

According to question

 \frac{x - 2 + 3}{x + 3}  =  \frac{4}{5}

 \frac{x + 1}{x + 3}  =  \frac{4}{5}

5(x + 1) = 4(x + 3)

5x + 5 = 4x + 12

x = 7

Numerator=5

Denominator=7

Fraction=

 \frac{5}{7}

Answered by Anonymous
13

\large{\mathfrak{\underline{\underline{\blue{Answer :-}}}}}

✯ a = 7

\large{\mathfrak{\underline{\underline{\red{Step-By-Step-Explanation:-}}}}}

__________________________

\large{\mathrm{\underline{\gray{Given:-}}}}

⇒ Let the denominator be a.

⇒ So, numerator be a - 2

\sf{Fraction \: = \:\frac{a - 2}{a}}______________(1)

\large{\mathrm{\underline{\gray{A.T.Q}}}}

\sf{\frac{a - 2 + 3}{a + 3} \: = \: \frac{4}{5}}

\sf{\frac{a + 1}{a + 3} \: = \: \frac{4}{5}}

\large{\mathrm{\underline{\gray{By \: Cross \: multiplication}}}}

\sf{5(a + 1) \: = \: 4(a + 3)}

\sf{5a + 5 \: = \: 4a + 12}

\sf{5a - 4a = 12 - 5}

\bf{a \: = \: 7}

____________[Put Value of a in (1)]

\bf{{\frac{7 \: - \: 5}{7}}}

\bf{Fraction \: = \: \frac{5}{7}}

\huge{\boxed{\boxed{Fraction\: = \: {\frac{5}{7}}}}}

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