Question

please solve and answer with explanation i will mark you brainliest

Answer 1

${\maltese \; {\underline{\underline{\textsf{\textbf{Given that :}}}}}}$

• The numerator of a number is greater than its denominator by 6
• If the numerator is decreased by 5 and the denominator it increased 2

* The new fraction obtained will be :

$\qquad \bigstar \; {\underline{\boxed{\pmb{\sf{ New \; Fraction = \frac{4}{5} }}}}}$

${\maltese \; {\underline{\underline{\textsf{\textbf{To Find :}}}}}}$

• The original fractional number

${\maltese \; {\underline{\underline{\textsf{\textbf{Assumptions :}}}}}}$

• Let the numerator of the fraction be x
• Let the denominator of the fraction be x - 6

${\maltese \; {\underline{\underline{\textsf{\textbf{Thereby :}}}}}}$

$\qquad \bigstar \; {\underline{\boxed{\pmb{\sf{ Original \; Fraction = \frac{x}{x-6} }}}}}$

${\maltese \; {\underline{\underline{\textsf{\textbf{Full Solution :}}}}}}$

★ According to the question :

$\longrightarrow \tt \dfrac{x - 5}{(x - 6 )+ 2} = \dfrac{4}{5}$

$\longrightarrow \tt 5 ({x - 5}) = 4{(x - 6 +2} )$

$\longrightarrow \tt {5x - 25} = {4x - 24 +8}$

$\longrightarrow \tt {5x - 4x} = { - 24 +8 + 25}$

$\longrightarrow \tt {5x - 4x} = { 9}$

$\longrightarrow {\purple{\underline{\boxed{ \frak{x =9 }}}}}$

${\maltese \; {\underline{\underline{\textsf{\textbf{Henceforth :}}}}}}$

$\nrightarrow \sf Numerator \; of \; the \; fraction = x = 9$

$\nrightarrow \sf Denominator \; of \; the \; fraction = x - 6 = 3$

${\maltese \; {\underline{\underline{\textsf{\textbf{Therefore :}}}}}}$

$\qquad \bigstar \; {\underline{\boxed{\pmb{\sf{ Original \; Fraction = \frac{9}{3} }}}}}$

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