Question

3. If 4 is added to the numerator and denominator it becomes 18/10 and if 6 is subtracted from the numerator and denominator it become 8/5. Find the fractions.

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

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$\green{\underline \bold{Given :}}$

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• Fraction becomes 18/10 when 4 is added to numerator and denominator.
• Fraction becomes 8/5 when 6 is subtracted from the numerator and denominator .

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$\red{\underline \bold{To \: Find:}}$

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• The fraction

$\large{\orange{\underline{\tt{Solution :-}}}}$

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Let the numerator be 'x'

Let the denominator be 'y'

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Original fraction will be :

⇛ $\rm\large{ \frac { x } { y } }$

$\purple{\underline \bold{According \: to \: the \ question :}}$

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⇛ $\rm \frac { x + 4} { y + 4} = \frac { 18 } { 10 }$

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⇛ $\rm \frac { x + 4} { y + 4} = \frac { 9 } { 5}$

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Cross multiplying

⇛ 5x + 20 = 9y + 36

⇛ 5x - 9y = 16 ------------(1)

Also,

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⇛ $\rm \frac { x - 6} { y - 6} = \frac { 8 } { 5 }$

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Cross multiplying

⇛ 5x - 30 = 8y - 48

⇛ -5x + 8y = 18 ------------(2)

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Adding (1) & (2)

We get,

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⇛ - y = 34

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⇛ y = -34

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Putting y = -34 in (2)

We get,

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⇛ -5x + 8(-34) = 18

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⇛ -5x - 272 = 18

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⇛ -5x = 290

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⇛ x = -58

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So the original fraction is $\sf\large{\frac { -58 } { -34 }}$