Question

A fraction is such that if the numerator is multiplied by 3 and the denominator is reduced by 3, we get 18 11, but if the numerator is increased by 8 and denominator is doubled, we get 2 5 . Find the fraction

Answer 1

Answer:

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Answer 2

Answer:

$\huge{\boxed{\sf{FRACTION=\frac{12}{25}}}}$

Step-by-step explanation:

$\huge{\boxed{\sf{SOLUTION-}}}$

$> > let \: numerator \: be = x \\ > > denominator \: be = y \\ > > fraction = \frac{x}{y} - - - - - (1) \\ according \: to \: question \\ \frac{3x}{y - 3} = \frac{18}{11} \\ 33x = 18y - 54 \\ 33x - 18y = - 54 - - - - - (2) \\ \frac{x + 8}{2y} = \frac{2}{5} \\ 5x + 40 = 4y \\ 5x = 4y - 40 \\ x = \frac{4y - 40}{5} - - - - - (3) \\ putting \: value \: f \: x \: in \: (2) \\ = )33 \times \frac{4y - 40}{5} - 18y = - 54 \\ = ) \frac{132y - 1320}{5} - \frac{18y}{1} = - 54 \\ = )132y - 1320 - 90y = - 270 \\ = )42y = - 270 + 1320 \\ = )42y = 1050 \\ = )y = \frac{1050}{42} \\ = )y = 25 - - - - - (4) \\ putting \: value \: of \: y \: in \: (3) \\ = ) x = \frac{4y - 40}{5} \\ = ) x = \frac{4 \times 25 - 40}{5} \\ = ) x = \frac{100 - 40}{5} \\ = ) x = \frac{60}{5} \\ = )x = 12 - - - - - (5) \\ putting \: value \: of \: x \: and \: y \: from \: (4) \: and \: (5) \: to \: (1) \\ fraction= \frac{x}{y} = \frac{12}{25}$

$\huge{\boxed{\sf{FRACTION=\frac{12}{25}}}}$