Question

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.

Answer 1

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=

$\frac{5}{7}$

Answer 2

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

✯ 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)]

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

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

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